{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0001", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261103, "batch_index": 0, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261102, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 13940, "truth_numerator": 2593, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 1, "B": 9}, "boxes": {"A": {"marked": 11, "unmarked": 23}, "B": {"marked": 7, "unmarked": 34}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.18601147776183644, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0002", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261103, "batch_index": 0, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261102, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 60, "truth_numerator": 59, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 59, "unmarked": 1}, "B": {"marked": 89, "unmarked": 8}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "A", "selection": "Choose one item uniformly at random from group A only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 0.9833333333333333, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0003", "question": "Is exactly one of the two selected items marked?", "source": {"actual_rng_seed": 20261103, "batch_index": 0, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261102, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 7, "truth_numerator": 4, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 3, "unmarked": 4}, "event": "exactly_one_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 0.5714285714285714, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0004", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261103, "batch_index": 0, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261102, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 1, "truth_numerator": 1, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 63, "unmarked": 4}, "B": {"marked": 60, "unmarked": 0}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "B", "selection": "Choose one item uniformly at random from group B only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 1.0, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0005", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261103, "batch_index": 0, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261102, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 60, "truth_numerator": 1, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 90, "unmarked": 0}, "B": {"marked": 1, "unmarked": 59}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "B", "selection": "Choose one item uniformly at random from group B only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 0.016666666666666666, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0006", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261103, "batch_index": 0, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261102, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 575, "truth_numerator": 406, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 9, "B": 1}, "boxes": {"A": {"marked": 16, "unmarked": 7}, "B": {"marked": 36, "unmarked": 9}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.7060869565217391, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0007", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261103, "batch_index": 0, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261102, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 1, "truth_numerator": 0, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 0, "unmarked": 30}, "B": {"marked": 23, "unmarked": 37}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "A", "selection": "Choose one item uniformly at random from group A only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 0.0, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0008", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261103, "batch_index": 0, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261102, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 104, "truth_numerator": 51, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 6, "B": 7}, "boxes": {"A": {"marked": 7, "unmarked": 9}, "B": {"marked": 15, "unmarked": 13}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.49038461538461536, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0009", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261103, "batch_index": 0, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261102, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 2, "truth_numerator": 1, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 10, "unmarked": 10}, "B": {"marked": 26, "unmarked": 0}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "A", "selection": "Choose one item uniformly at random from group A only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 0.5, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0010", "question": "Are both selected items marked?", "source": {"actual_rng_seed": 20261103, "batch_index": 0, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261102, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 247, "truth_numerator": 210, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 36, "unmarked": 3}, "event": "both_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 0.8502024291497976, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0011", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261103, "batch_index": 0, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261102, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 1, "truth_numerator": 0, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 0, "unmarked": 50}, "B": {"marked": 67, "unmarked": 31}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "A", "selection": "Choose one item uniformly at random from group A only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 0.0, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0012", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261103, "batch_index": 0, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261102, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 9594, "truth_numerator": 5323, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 5, "B": 8}, "boxes": {"A": {"marked": 14, "unmarked": 22}, "B": {"marked": 27, "unmarked": 14}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.5548259328747134, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0013", "question": "Is at least one of the two selected items marked?", "source": {"actual_rng_seed": 20261103, "batch_index": 0, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261102, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 741, "truth_numerator": 740, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 37, "unmarked": 2}, "event": "at_least_one_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 0.9986504723346828, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0014", "question": "Are both selected items marked?", "source": {"actual_rng_seed": 20261103, "batch_index": 0, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261102, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 155, "truth_numerator": 126, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 28, "unmarked": 3}, "event": "both_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 0.8129032258064516, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0015", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261103, "batch_index": 0, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261102, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 319, "truth_numerator": 272, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 7, "B": 4}, "boxes": {"A": {"marked": 28, "unmarked": 1}, "B": {"marked": 19, "unmarked": 10}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.8526645768025078, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0016", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261103, "batch_index": 0, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261102, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 220, "truth_numerator": 213, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 9, "B": 2}, "boxes": {"A": {"marked": 45, "unmarked": 0}, "B": {"marked": 33, "unmarked": 7}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.9681818181818181, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0017", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261103, "batch_index": 0, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261102, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 5, "truth_numerator": 1, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 43, "unmarked": 25}, "B": {"marked": 8, "unmarked": 32}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "B", "selection": "Choose one item uniformly at random from group B only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 0.2, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0018", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261103, "batch_index": 0, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261102, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 40, "truth_numerator": 1, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 29, "unmarked": 36}, "B": {"marked": 1, "unmarked": 39}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "B", "selection": "Choose one item uniformly at random from group B only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 0.025, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0019", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261103, "batch_index": 0, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261102, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 64, "truth_numerator": 33, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 7, "B": 9}, "boxes": {"A": {"marked": 0, "unmarked": 8}, "B": {"marked": 11, "unmarked": 1}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.515625, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0020", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261103, "batch_index": 0, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261102, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 21, "truth_numerator": 8, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 8, "B": 4}, "boxes": {"A": {"marked": 10, "unmarked": 39}, "B": {"marked": 36, "unmarked": 13}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.38095238095238093, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0021", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261103, "batch_index": 0, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261102, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 20, "truth_numerator": 1, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 1, "unmarked": 19}, "B": {"marked": 5, "unmarked": 25}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "A", "selection": "Choose one item uniformly at random from group A only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 0.05, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0022", "question": "Are both selected items marked?", "source": {"actual_rng_seed": 20261103, "batch_index": 0, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261102, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 10, "truth_numerator": 1, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 2, "unmarked": 3}, "event": "both_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 0.1, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0023", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261103, "batch_index": 0, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261102, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 60, "truth_numerator": 31, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 1, "unmarked": 26}, "B": {"marked": 31, "unmarked": 29}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "B", "selection": "Choose one item uniformly at random from group B only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 0.5166666666666667, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0024", "question": "Is at least one of the two selected items marked?", "source": {"actual_rng_seed": 20261103, "batch_index": 0, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261102, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 77, "truth_numerator": 26, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 4, "unmarked": 18}, "event": "at_least_one_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 0.33766233766233766, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0025", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261103, "batch_index": 0, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261102, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 495, "truth_numerator": 191, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 2, "B": 9}, "boxes": {"A": {"marked": 28, "unmarked": 17}, "B": {"marked": 2, "unmarked": 4}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.38585858585858585, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0026", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261103, "batch_index": 0, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261102, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 38, "truth_numerator": 25, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 6, "B": 1}, "boxes": {"A": {"marked": 27, "unmarked": 9}, "B": {"marked": 2, "unmarked": 17}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.6578947368421053, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0027", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261103, "batch_index": 0, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261102, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 30, "truth_numerator": 1, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 1, "unmarked": 29}, "B": {"marked": 15, "unmarked": 62}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "A", "selection": "Choose one item uniformly at random from group A only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 0.03333333333333333, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0028", "question": "Are both selected items marked?", "source": {"actual_rng_seed": 20261103, "batch_index": 0, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261102, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 247, "truth_numerator": 5, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 6, "unmarked": 33}, "event": "both_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 0.020242914979757085, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0029", "question": "Is exactly one of the two selected items marked?", "source": {"actual_rng_seed": 20261103, "batch_index": 0, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261102, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 77, "truth_numerator": 32, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 16, "unmarked": 6}, "event": "exactly_one_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 0.4155844155844156, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0030", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261103, "batch_index": 0, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261102, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 1, "truth_numerator": 1, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 20, "unmarked": 0}, "B": {"marked": 27, "unmarked": 0}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "A", "selection": "Choose one item uniformly at random from group A only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 1.0, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0031", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261103, "batch_index": 0, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261102, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 20, "truth_numerator": 13, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 2, "B": 2}, "boxes": {"A": {"marked": 6, "unmarked": 4}, "B": {"marked": 14, "unmarked": 6}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.65, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0032", "question": "Are both selected items marked?", "source": {"actual_rng_seed": 20261103, "batch_index": 0, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261102, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 30, "truth_numerator": 1, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 7, "unmarked": 29}, "event": "both_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 0.03333333333333333, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0033", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261103, "batch_index": 0, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261102, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 1, "truth_numerator": 0, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 0, "unmarked": 40}, "B": {"marked": 6, "unmarked": 11}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "A", "selection": "Choose one item uniformly at random from group A only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 0.0, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0034", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261103, "batch_index": 0, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261102, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 20, "truth_numerator": 19, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 19, "unmarked": 1}, "B": {"marked": 63, "unmarked": 22}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "A", "selection": "Choose one item uniformly at random from group A only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 0.95, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0035", "question": "Is exactly one of the two selected items marked?", "source": {"actual_rng_seed": 20261103, "batch_index": 0, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261102, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 6, "truth_numerator": 1, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 11, "unmarked": 1}, "event": "exactly_one_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 0.16666666666666666, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0036", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261103, "batch_index": 0, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261102, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 3663, "truth_numerator": 1085, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 2, "B": 9}, "boxes": {"A": {"marked": 7, "unmarked": 2}, "B": {"marked": 7, "unmarked": 30}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.29620529620529623, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0037", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261103, "batch_index": 0, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261102, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 667, "truth_numerator": 173, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 2, "B": 9}, "boxes": {"A": {"marked": 13, "unmarked": 16}, "B": {"marked": 10, "unmarked": 36}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.2593703148425787, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0038", "question": "Is at least one of the two selected items marked?", "source": {"actual_rng_seed": 20261103, "batch_index": 0, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261102, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 260, "truth_numerator": 203, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 21, "unmarked": 19}, "event": "at_least_one_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 0.7807692307692308, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0039", "question": "Is exactly one of the two selected items marked?", "source": {"actual_rng_seed": 20261103, "batch_index": 0, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261102, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 28, "truth_numerator": 15, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 5, "unmarked": 3}, "event": "exactly_one_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 0.5357142857142857, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0040", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261103, "batch_index": 0, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261102, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 5, "truth_numerator": 1, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 12, "unmarked": 48}, "B": {"marked": 16, "unmarked": 76}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "A", "selection": "Choose one item uniformly at random from group A only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 0.2, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0041", "question": "Is at least one of the two selected items marked?", "source": {"actual_rng_seed": 20261103, "batch_index": 0, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261102, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 189, "truth_numerator": 121, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 11, "unmarked": 17}, "event": "at_least_one_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 0.6402116402116402, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0042", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261103, "batch_index": 0, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261102, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 5, "truth_numerator": 1, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 12, "unmarked": 48}, "B": {"marked": 2, "unmarked": 41}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "A", "selection": "Choose one item uniformly at random from group A only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 0.2, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0043", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261103, "batch_index": 0, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261102, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 28, "truth_numerator": 19, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 5, "B": 9}, "boxes": {"A": {"marked": 15, "unmarked": 0}, "B": {"marked": 15, "unmarked": 15}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.6785714285714286, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0044", "question": "Is exactly one of the two selected items marked?", "source": {"actual_rng_seed": 20261103, "batch_index": 0, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261102, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 351, "truth_numerator": 170, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 17, "unmarked": 10}, "event": "exactly_one_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 0.4843304843304843, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0045", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261103, "batch_index": 0, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261102, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 5032, "truth_numerator": 1827, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 1, "B": 7}, "boxes": {"A": {"marked": 14, "unmarked": 3}, "B": {"marked": 11, "unmarked": 26}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.36307631160572335, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0046", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261103, "batch_index": 0, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261102, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 2, "truth_numerator": 1, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 15, "unmarked": 15}, "B": {"marked": 20, "unmarked": 14}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "A", "selection": "Choose one item uniformly at random from group A only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 0.5, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0047", "question": "Is exactly one of the two selected items marked?", "source": {"actual_rng_seed": 20261103, "batch_index": 0, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261102, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 253, "truth_numerator": 76, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 19, "unmarked": 4}, "event": "exactly_one_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 0.30039525691699603, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0048", "question": "Are both selected items marked?", "source": {"actual_rng_seed": 20261103, "batch_index": 0, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261102, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 46, "truth_numerator": 11, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 12, "unmarked": 12}, "event": "both_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 0.2391304347826087, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0049", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261103, "batch_index": 0, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261102, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 5, "truth_numerator": 1, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 33, "unmarked": 4}, "B": {"marked": 4, "unmarked": 16}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "B", "selection": "Choose one item uniformly at random from group B only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 0.2, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0050", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261103, "batch_index": 0, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261102, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 98, "truth_numerator": 39, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 2, "B": 6}, "boxes": {"A": {"marked": 0, "unmarked": 5}, "B": {"marked": 26, "unmarked": 23}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.3979591836734694, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0051", "question": "Is at least one of the two selected items marked?", "source": {"actual_rng_seed": 20261103, "batch_index": 0, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261102, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 1, "truth_numerator": 1, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 27, "unmarked": 0}, "event": "at_least_one_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 1.0, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0052", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261103, "batch_index": 0, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261102, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 1, "truth_numerator": 1, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 50, "unmarked": 0}, "B": {"marked": 30, "unmarked": 11}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "A", "selection": "Choose one item uniformly at random from group A only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 1.0, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0053", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261103, "batch_index": 0, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261102, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 2, "truth_numerator": 1, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 11, "unmarked": 5}, "B": {"marked": 30, "unmarked": 30}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "B", "selection": "Choose one item uniformly at random from group B only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 0.5, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0054", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261103, "batch_index": 0, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261102, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 1040, "truth_numerator": 437, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 7, "B": 9}, "boxes": {"A": {"marked": 2, "unmarked": 3}, "B": {"marked": 17, "unmarked": 22}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.4201923076923077, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0055", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261103, "batch_index": 0, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261102, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 30, "truth_numerator": 11, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 6, "B": 9}, "boxes": {"A": {"marked": 5, "unmarked": 5}, "B": {"marked": 10, "unmarked": 26}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.36666666666666664, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0056", "question": "Is exactly one of the two selected items marked?", "source": {"actual_rng_seed": 20261103, "batch_index": 0, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261102, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 11, "truth_numerator": 1, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 21, "unmarked": 1}, "event": "exactly_one_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 0.09090909090909091, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0057", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261103, "batch_index": 0, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261102, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 7260, "truth_numerator": 3433, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 9, "B": 2}, "boxes": {"A": {"marked": 9, "unmarked": 11}, "B": {"marked": 19, "unmarked": 14}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.47286501377410467, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0058", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261103, "batch_index": 0, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261102, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 9, "truth_numerator": 5, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 5, "B": 3}, "boxes": {"A": {"marked": 18, "unmarked": 9}, "B": {"marked": 10, "unmarked": 17}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.5555555555555556, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0059", "question": "Are both selected items marked?", "source": {"actual_rng_seed": 20261103, "batch_index": 0, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261102, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 19, "truth_numerator": 1, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 5, "unmarked": 15}, "event": "both_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 0.05263157894736842, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0060", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261104, "batch_index": 1, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261103, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 3, "truth_numerator": 2, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 5, "B": 7}, "boxes": {"A": {"marked": 1, "unmarked": 4}, "B": {"marked": 27, "unmarked": 0}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.6666666666666666, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0061", "question": "Is at least one of the two selected items marked?", "source": {"actual_rng_seed": 20261104, "batch_index": 1, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261103, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 92, "truth_numerator": 35, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 5, "unmarked": 19}, "event": "at_least_one_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 0.3804347826086957, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0062", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261104, "batch_index": 1, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261103, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 5, "truth_numerator": 4, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 6, "B": 4}, "boxes": {"A": {"marked": 43, "unmarked": 0}, "B": {"marked": 14, "unmarked": 14}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.8, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0063", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261104, "batch_index": 1, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261103, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 60, "truth_numerator": 31, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 31, "unmarked": 29}, "B": {"marked": 51, "unmarked": 8}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "A", "selection": "Choose one item uniformly at random from group A only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 0.5166666666666667, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0064", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261104, "batch_index": 1, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261103, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 17, "truth_numerator": 4, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 8, "B": 6}, "boxes": {"A": {"marked": 7, "unmarked": 10}, "B": {"marked": 0, "unmarked": 41}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.23529411764705882, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0065", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261104, "batch_index": 1, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261103, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 2, "truth_numerator": 1, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 15, "unmarked": 15}, "B": {"marked": 10, "unmarked": 0}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "A", "selection": "Choose one item uniformly at random from group A only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 0.5, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0066", "question": "Is exactly one of the two selected items marked?", "source": {"actual_rng_seed": 20261104, "batch_index": 1, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261103, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 5, "truth_numerator": 3, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 3, "unmarked": 3}, "event": "exactly_one_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 0.6, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0067", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261104, "batch_index": 1, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261103, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 5704, "truth_numerator": 379, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 5, "B": 3}, "boxes": {"A": {"marked": 2, "unmarked": 21}, "B": {"marked": 1, "unmarked": 30}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.0664446002805049, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0068", "question": "Is at least one of the two selected items marked?", "source": {"actual_rng_seed": 20261104, "batch_index": 1, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261103, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 1, "truth_numerator": 0, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 0, "unmarked": 15}, "event": "at_least_one_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 0.0, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0069", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261104, "batch_index": 1, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261103, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 40, "truth_numerator": 21, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 63, "unmarked": 11}, "B": {"marked": 21, "unmarked": 19}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "B", "selection": "Choose one item uniformly at random from group B only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 0.525, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0070", "question": "Is exactly one of the two selected items marked?", "source": {"actual_rng_seed": 20261104, "batch_index": 1, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261103, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 20, "truth_numerator": 1, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 39, "unmarked": 1}, "event": "exactly_one_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 0.05, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0071", "question": "Is exactly one of the two selected items marked?", "source": {"actual_rng_seed": 20261104, "batch_index": 1, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261103, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 253, "truth_numerator": 42, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 21, "unmarked": 2}, "event": "exactly_one_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 0.16600790513833993, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0072", "question": "Is at least one of the two selected items marked?", "source": {"actual_rng_seed": 20261104, "batch_index": 1, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261103, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 300, "truth_numerator": 299, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 23, "unmarked": 2}, "event": "at_least_one_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 0.9966666666666667, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0073", "question": "Is at least one of the two selected items marked?", "source": {"actual_rng_seed": 20261104, "batch_index": 1, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261103, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 861, "truth_numerator": 536, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 16, "unmarked": 26}, "event": "at_least_one_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 0.6225319396051103, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0074", "question": "Are both selected items marked?", "source": {"actual_rng_seed": 20261104, "batch_index": 1, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261103, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 41, "truth_numerator": 39, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 40, "unmarked": 1}, "event": "both_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 0.9512195121951219, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0075", "question": "Are both selected items marked?", "source": {"actual_rng_seed": 20261104, "batch_index": 1, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261103, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 1, "truth_numerator": 0, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 1, "unmarked": 4}, "event": "both_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 0.0, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0076", "question": "Are both selected items marked?", "source": {"actual_rng_seed": 20261104, "batch_index": 1, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261103, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 15, "truth_numerator": 14, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 29, "unmarked": 1}, "event": "both_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 0.9333333333333333, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0077", "question": "Are both selected items marked?", "source": {"actual_rng_seed": 20261104, "batch_index": 1, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261103, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 946, "truth_numerator": 171, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 19, "unmarked": 25}, "event": "both_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 0.18076109936575052, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0078", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261104, "batch_index": 1, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261103, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 150, "truth_numerator": 61, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 9, "B": 6}, "boxes": {"A": {"marked": 6, "unmarked": 14}, "B": {"marked": 17, "unmarked": 13}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.4066666666666667, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0079", "question": "Is exactly one of the two selected items marked?", "source": {"actual_rng_seed": 20261104, "batch_index": 1, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261103, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 17, "truth_numerator": 9, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 9, "unmarked": 8}, "event": "exactly_one_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 0.5294117647058824, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0080", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261104, "batch_index": 1, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261103, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 3025, "truth_numerator": 1682, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 8, "B": 3}, "boxes": {"A": {"marked": 28, "unmarked": 22}, "B": {"marked": 6, "unmarked": 5}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.5560330578512397, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0081", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261104, "batch_index": 1, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261103, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 30, "truth_numerator": 29, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 29, "unmarked": 1}, "B": {"marked": 5, "unmarked": 53}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "A", "selection": "Choose one item uniformly at random from group A only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 0.9666666666666667, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0082", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261104, "batch_index": 1, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261103, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 4131, "truth_numerator": 2989, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 5, "B": 4}, "boxes": {"A": {"marked": 25, "unmarked": 2}, "B": {"marked": 8, "unmarked": 9}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.7235536189784556, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0083", "question": "Are both selected items marked?", "source": {"actual_rng_seed": 20261104, "batch_index": 1, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261103, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 11, "truth_numerator": 3, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 6, "unmarked": 5}, "event": "both_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 0.2727272727272727, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0084", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261104, "batch_index": 1, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261103, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 460, "truth_numerator": 81, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 1, "B": 9}, "boxes": {"A": {"marked": 0, "unmarked": 16}, "B": {"marked": 9, "unmarked": 37}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.17608695652173914, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0085", "question": "Are both selected items marked?", "source": {"actual_rng_seed": 20261104, "batch_index": 1, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261103, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 17, "truth_numerator": 16, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 33, "unmarked": 1}, "event": "both_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 0.9411764705882353, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0086", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261104, "batch_index": 1, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261103, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 20, "truth_numerator": 11, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 46, "unmarked": 4}, "B": {"marked": 11, "unmarked": 9}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "B", "selection": "Choose one item uniformly at random from group B only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 0.55, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0087", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261104, "batch_index": 1, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261103, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 40, "truth_numerator": 39, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 39, "unmarked": 1}, "B": {"marked": 13, "unmarked": 34}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "A", "selection": "Choose one item uniformly at random from group A only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 0.975, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0088", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261104, "batch_index": 1, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261103, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 30, "truth_numerator": 29, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 0, "unmarked": 78}, "B": {"marked": 29, "unmarked": 1}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "B", "selection": "Choose one item uniformly at random from group B only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 0.9666666666666667, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0089", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261104, "batch_index": 1, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261103, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 60, "truth_numerator": 59, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 59, "unmarked": 1}, "B": {"marked": 68, "unmarked": 0}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "A", "selection": "Choose one item uniformly at random from group A only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 0.9833333333333333, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0090", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261104, "batch_index": 1, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261103, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 10879, "truth_numerator": 2650, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 8, "B": 3}, "boxes": {"A": {"marked": 13, "unmarked": 30}, "B": {"marked": 4, "unmarked": 42}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.24358856512547108, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0091", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261104, "batch_index": 1, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261103, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 5687, "truth_numerator": 447, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 6, "B": 5}, "boxes": {"A": {"marked": 3, "unmarked": 30}, "B": {"marked": 3, "unmarked": 44}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.07860031651134165, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0092", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261104, "batch_index": 1, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261103, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 1, "truth_numerator": 0, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 44, "unmarked": 31}, "B": {"marked": 0, "unmarked": 60}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "B", "selection": "Choose one item uniformly at random from group B only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 0.0, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0093", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261104, "batch_index": 1, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261103, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 7, "truth_numerator": 1, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 1, "B": 6}, "boxes": {"A": {"marked": 25, "unmarked": 0}, "B": {"marked": 0, "unmarked": 25}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.14285714285714285, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0094", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261104, "batch_index": 1, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261103, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 50, "truth_numerator": 1, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 6, "unmarked": 25}, "B": {"marked": 1, "unmarked": 49}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "B", "selection": "Choose one item uniformly at random from group B only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 0.02, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0095", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261104, "batch_index": 1, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261103, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 684, "truth_numerator": 497, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 7, "B": 1}, "boxes": {"A": {"marked": 7, "unmarked": 2}, "B": {"marked": 7, "unmarked": 12}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.7266081871345029, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0096", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261104, "batch_index": 1, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261103, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 280, "truth_numerator": 233, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 2, "B": 4}, "boxes": {"A": {"marked": 37, "unmarked": 3}, "B": {"marked": 11, "unmarked": 3}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.8321428571428572, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0097", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261104, "batch_index": 1, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261103, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 5, "truth_numerator": 2, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 4, "B": 1}, "boxes": {"A": {"marked": 9, "unmarked": 27}, "B": {"marked": 5, "unmarked": 0}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.4, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0098", "question": "Is at least one of the two selected items marked?", "source": {"actual_rng_seed": 20261104, "batch_index": 1, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261103, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 20, "truth_numerator": 7, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 3, "unmarked": 13}, "event": "at_least_one_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 0.35, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0099", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261104, "batch_index": 1, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261103, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 374, "truth_numerator": 173, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 4, "B": 4}, "boxes": {"A": {"marked": 5, "unmarked": 6}, "B": {"marked": 8, "unmarked": 9}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.4625668449197861, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0100", "question": "Is exactly one of the two selected items marked?", "source": {"actual_rng_seed": 20261104, "batch_index": 1, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261103, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 57, "truth_numerator": 26, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 13, "unmarked": 26}, "event": "exactly_one_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 0.45614035087719296, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0101", "question": "Are both selected items marked?", "source": {"actual_rng_seed": 20261104, "batch_index": 1, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261103, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 95, "truth_numerator": 18, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 9, "unmarked": 11}, "event": "both_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 0.18947368421052632, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0102", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261104, "batch_index": 1, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261103, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 50, "truth_numerator": 49, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 49, "unmarked": 1}, "B": {"marked": 9, "unmarked": 28}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "A", "selection": "Choose one item uniformly at random from group A only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 0.98, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0103", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261104, "batch_index": 1, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261103, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 2, "truth_numerator": 1, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 25, "unmarked": 25}, "B": {"marked": 15, "unmarked": 19}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "A", "selection": "Choose one item uniformly at random from group A only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 0.5, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0104", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261104, "batch_index": 1, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261103, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 25, "truth_numerator": 13, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 26, "unmarked": 24}, "B": {"marked": 40, "unmarked": 27}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "A", "selection": "Choose one item uniformly at random from group A only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 0.52, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0105", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261104, "batch_index": 1, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261103, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 45, "truth_numerator": 29, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 5, "B": 8}, "boxes": {"A": {"marked": 7, "unmarked": 0}, "B": {"marked": 19, "unmarked": 26}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.6444444444444445, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0106", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261104, "batch_index": 1, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261103, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 5, "truth_numerator": 1, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 12, "unmarked": 48}, "B": {"marked": 55, "unmarked": 39}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "A", "selection": "Choose one item uniformly at random from group A only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 0.2, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0107", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261104, "batch_index": 1, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261103, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 2, "truth_numerator": 1, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 30, "unmarked": 30}, "B": {"marked": 30, "unmarked": 70}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "A", "selection": "Choose one item uniformly at random from group A only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 0.5, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0108", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261104, "batch_index": 1, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261103, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 7920, "truth_numerator": 4157, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 1, "B": 5}, "boxes": {"A": {"marked": 29, "unmarked": 11}, "B": {"marked": 16, "unmarked": 17}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.5248737373737373, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0109", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261104, "batch_index": 1, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261103, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 5, "truth_numerator": 1, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 6, "unmarked": 24}, "B": {"marked": 31, "unmarked": 26}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "A", "selection": "Choose one item uniformly at random from group A only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 0.2, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0110", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261104, "batch_index": 1, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261103, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 5, "truth_numerator": 1, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 12, "unmarked": 48}, "B": {"marked": 5, "unmarked": 13}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "A", "selection": "Choose one item uniformly at random from group A only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 0.2, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0111", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261104, "batch_index": 1, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261103, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 84, "truth_numerator": 83, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 1, "B": 3}, "boxes": {"A": {"marked": 20, "unmarked": 1}, "B": {"marked": 25, "unmarked": 0}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.9880952380952381, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0112", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261104, "batch_index": 1, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261103, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 20, "truth_numerator": 11, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 10, "unmarked": 13}, "B": {"marked": 11, "unmarked": 9}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "B", "selection": "Choose one item uniformly at random from group B only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 0.55, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0113", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261104, "batch_index": 1, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261103, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 5, "truth_numerator": 1, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 8, "unmarked": 32}, "B": {"marked": 52, "unmarked": 38}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "A", "selection": "Choose one item uniformly at random from group A only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 0.2, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0114", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261104, "batch_index": 1, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261103, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 2, "truth_numerator": 1, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 25, "unmarked": 25}, "B": {"marked": 7, "unmarked": 6}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "A", "selection": "Choose one item uniformly at random from group A only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 0.5, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0115", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261104, "batch_index": 1, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261103, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 1904, "truth_numerator": 723, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 3, "B": 4}, "boxes": {"A": {"marked": 1, "unmarked": 15}, "B": {"marked": 21, "unmarked": 13}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.3797268907563025, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0116", "question": "Is exactly one of the two selected items marked?", "source": {"actual_rng_seed": 20261104, "batch_index": 1, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261103, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 7, "truth_numerator": 2, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 1, "unmarked": 6}, "event": "exactly_one_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 0.2857142857142857, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0117", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261104, "batch_index": 1, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261103, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 3267, "truth_numerator": 1279, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 8, "B": 3}, "boxes": {"A": {"marked": 13, "unmarked": 14}, "B": {"marked": 5, "unmarked": 28}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.39149066421793693, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0118", "question": "Is at least one of the two selected items marked?", "source": {"actual_rng_seed": 20261104, "batch_index": 1, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261103, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 1, "truth_numerator": 1, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 43, "unmarked": 0}, "event": "at_least_one_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 1.0, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0119", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261105, "batch_index": 2, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261104, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 88, "truth_numerator": 5, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 3, "B": 3}, "boxes": {"A": {"marked": 0, "unmarked": 8}, "B": {"marked": 5, "unmarked": 39}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.056818181818181816, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0120", "question": "Is at least one of the two selected items marked?", "source": {"actual_rng_seed": 20261105, "batch_index": 2, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261104, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 187, "truth_numerator": 152, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 19, "unmarked": 15}, "event": "at_least_one_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 0.8128342245989305, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0121", "question": "Is at least one of the two selected items marked?", "source": {"actual_rng_seed": 20261105, "batch_index": 2, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261104, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 117, "truth_numerator": 112, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 21, "unmarked": 6}, "event": "at_least_one_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 0.9572649572649573, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0122", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261105, "batch_index": 2, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261104, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 572, "truth_numerator": 283, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 6, "B": 6}, "boxes": {"A": {"marked": 15, "unmarked": 7}, "B": {"marked": 8, "unmarked": 18}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.49475524475524474, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0123", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261105, "batch_index": 2, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261104, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 1216, "truth_numerator": 737, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 9, "B": 3}, "boxes": {"A": {"marked": 18, "unmarked": 14}, "B": {"marked": 28, "unmarked": 10}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.6060855263157895, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0124", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261105, "batch_index": 2, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261104, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 91, "truth_numerator": 64, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 4, "B": 9}, "boxes": {"A": {"marked": 44, "unmarked": 0}, "B": {"marked": 16, "unmarked": 12}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.7032967032967034, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0125", "question": "Are both selected items marked?", "source": {"actual_rng_seed": 20261105, "batch_index": 2, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261104, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 820, "truth_numerator": 703, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 38, "unmarked": 3}, "event": "both_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 0.8573170731707317, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0126", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261105, "batch_index": 2, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261104, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 25, "truth_numerator": 13, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 21, "unmarked": 70}, "B": {"marked": 26, "unmarked": 24}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "B", "selection": "Choose one item uniformly at random from group B only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 0.52, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0127", "question": "Are both selected items marked?", "source": {"actual_rng_seed": 20261105, "batch_index": 2, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261104, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 561, "truth_numerator": 325, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 26, "unmarked": 8}, "event": "both_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 0.5793226381461676, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0128", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261105, "batch_index": 2, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261104, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 20, "truth_numerator": 19, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 19, "unmarked": 1}, "B": {"marked": 76, "unmarked": 13}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "A", "selection": "Choose one item uniformly at random from group A only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 0.95, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0129", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261105, "batch_index": 2, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261104, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 30, "truth_numerator": 1, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 4, "unmarked": 9}, "B": {"marked": 1, "unmarked": 29}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "B", "selection": "Choose one item uniformly at random from group B only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 0.03333333333333333, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0130", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261105, "batch_index": 2, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261104, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 1, "truth_numerator": 1, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 30, "unmarked": 0}, "B": {"marked": 19, "unmarked": 78}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "A", "selection": "Choose one item uniformly at random from group A only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 1.0, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0131", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261105, "batch_index": 2, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261104, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 884, "truth_numerator": 387, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 9, "B": 9}, "boxes": {"A": {"marked": 1, "unmarked": 33}, "B": {"marked": 22, "unmarked": 4}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.43778280542986425, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0132", "question": "Is exactly one of the two selected items marked?", "source": {"actual_rng_seed": 20261105, "batch_index": 2, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261104, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 21, "truth_numerator": 8, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 5, "unmarked": 16}, "event": "exactly_one_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 0.38095238095238093, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0133", "question": "Is exactly one of the two selected items marked?", "source": {"actual_rng_seed": 20261105, "batch_index": 2, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261104, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 1, "truth_numerator": 0, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 6, "unmarked": 0}, "event": "exactly_one_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 0.0, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0134", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261105, "batch_index": 2, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261104, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 20, "truth_numerator": 19, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 19, "unmarked": 1}, "B": {"marked": 65, "unmarked": 23}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "A", "selection": "Choose one item uniformly at random from group A only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 0.95, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0135", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261105, "batch_index": 2, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261104, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 15, "truth_numerator": 8, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 12, "unmarked": 7}, "B": {"marked": 16, "unmarked": 14}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "B", "selection": "Choose one item uniformly at random from group B only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 0.5333333333333333, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0136", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261105, "batch_index": 2, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261104, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 99, "truth_numerator": 64, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 6, "B": 3}, "boxes": {"A": {"marked": 28, "unmarked": 16}, "B": {"marked": 14, "unmarked": 7}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.6464646464646465, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0137", "question": "Is at least one of the two selected items marked?", "source": {"actual_rng_seed": 20261105, "batch_index": 2, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261104, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 153, "truth_numerator": 125, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 10, "unmarked": 8}, "event": "at_least_one_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 0.8169934640522876, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0138", "question": "Is exactly one of the two selected items marked?", "source": {"actual_rng_seed": 20261105, "batch_index": 2, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261104, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 1, "truth_numerator": 0, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 30, "unmarked": 0}, "event": "exactly_one_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 0.0, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0139", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261105, "batch_index": 2, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261104, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 405, "truth_numerator": 127, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 2, "B": 7}, "boxes": {"A": {"marked": 32, "unmarked": 13}, "B": {"marked": 10, "unmarked": 40}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.3135802469135803, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0140", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261105, "batch_index": 2, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261104, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 2288, "truth_numerator": 475, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 7, "B": 4}, "boxes": {"A": {"marked": 1, "unmarked": 15}, "B": {"marked": 12, "unmarked": 14}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.2076048951048951, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0141", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261105, "batch_index": 2, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261104, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 60, "truth_numerator": 59, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 25, "unmarked": 17}, "B": {"marked": 59, "unmarked": 1}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "B", "selection": "Choose one item uniformly at random from group B only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 0.9833333333333333, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0142", "question": "Are both selected items marked?", "source": {"actual_rng_seed": 20261105, "batch_index": 2, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261104, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 496, "truth_numerator": 253, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 23, "unmarked": 9}, "event": "both_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 0.5100806451612904, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0143", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261105, "batch_index": 2, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261104, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 1, "truth_numerator": 0, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 0, "unmarked": 20}, "B": {"marked": 5, "unmarked": 60}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "A", "selection": "Choose one item uniformly at random from group A only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 0.0, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0144", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261105, "batch_index": 2, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261104, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 2, "truth_numerator": 1, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 15, "unmarked": 9}, "B": {"marked": 30, "unmarked": 30}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "B", "selection": "Choose one item uniformly at random from group B only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 0.5, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0145", "question": "Is exactly one of the two selected items marked?", "source": {"actual_rng_seed": 20261105, "batch_index": 2, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261104, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 31, "truth_numerator": 16, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 16, "unmarked": 15}, "event": "exactly_one_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 0.5161290322580645, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0146", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261105, "batch_index": 2, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261104, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 1, "truth_numerator": 1, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 40, "unmarked": 0}, "B": {"marked": 15, "unmarked": 1}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "A", "selection": "Choose one item uniformly at random from group A only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 1.0, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0147", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261105, "batch_index": 2, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261104, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 40, "truth_numerator": 1, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 1, "unmarked": 39}, "B": {"marked": 37, "unmarked": 28}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "A", "selection": "Choose one item uniformly at random from group A only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 0.025, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0148", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261105, "batch_index": 2, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261104, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 25, "truth_numerator": 13, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 26, "unmarked": 24}, "B": {"marked": 30, "unmarked": 3}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "A", "selection": "Choose one item uniformly at random from group A only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 0.52, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0149", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261105, "batch_index": 2, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261104, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 1, "truth_numerator": 0, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 32, "unmarked": 52}, "B": {"marked": 0, "unmarked": 30}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "B", "selection": "Choose one item uniformly at random from group B only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 0.0, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0150", "question": "Is at least one of the two selected items marked?", "source": {"actual_rng_seed": 20261105, "batch_index": 2, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261104, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 19, "truth_numerator": 18, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 15, "unmarked": 5}, "event": "at_least_one_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 0.9473684210526315, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0151", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261105, "batch_index": 2, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261104, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 1, "truth_numerator": 1, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 5, "unmarked": 60}, "B": {"marked": 60, "unmarked": 0}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "B", "selection": "Choose one item uniformly at random from group B only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 1.0, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0152", "question": "Are both selected items marked?", "source": {"actual_rng_seed": 20261105, "batch_index": 2, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261104, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 741, "truth_numerator": 136, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 17, "unmarked": 22}, "event": "both_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 0.18353576248313092, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0153", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261105, "batch_index": 2, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261104, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 26, "truth_numerator": 7, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 8, "B": 5}, "boxes": {"A": {"marked": 8, "unmarked": 24}, "B": {"marked": 9, "unmarked": 21}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.2692307692307692, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0154", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261105, "batch_index": 2, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261104, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 225, "truth_numerator": 14, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 6, "B": 4}, "boxes": {"A": {"marked": 0, "unmarked": 45}, "B": {"marked": 7, "unmarked": 38}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.06222222222222222, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0155", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261105, "batch_index": 2, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261104, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 40, "truth_numerator": 1, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 58, "unmarked": 36}, "B": {"marked": 1, "unmarked": 39}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "B", "selection": "Choose one item uniformly at random from group B only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 0.025, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0156", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261105, "batch_index": 2, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261104, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 1, "truth_numerator": 1, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 34, "unmarked": 62}, "B": {"marked": 60, "unmarked": 0}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "B", "selection": "Choose one item uniformly at random from group B only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 1.0, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0157", "question": "Is exactly one of the two selected items marked?", "source": {"actual_rng_seed": 20261105, "batch_index": 2, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261104, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 1, "truth_numerator": 0, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 0, "unmarked": 9}, "event": "exactly_one_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 0.0, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0158", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261105, "batch_index": 2, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261104, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 49, "truth_numerator": 31, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 5, "B": 2}, "boxes": {"A": {"marked": 31, "unmarked": 4}, "B": {"marked": 0, "unmarked": 6}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.6326530612244898, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0159", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261105, "batch_index": 2, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261104, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 1, "truth_numerator": 0, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 14, "unmarked": 15}, "B": {"marked": 0, "unmarked": 50}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "B", "selection": "Choose one item uniformly at random from group B only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 0.0, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0160", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261105, "batch_index": 2, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261104, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 204, "truth_numerator": 115, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 5, "B": 5}, "boxes": {"A": {"marked": 5, "unmarked": 12}, "B": {"marked": 20, "unmarked": 4}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.5637254901960784, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0161", "question": "Is at least one of the two selected items marked?", "source": {"actual_rng_seed": 20261105, "batch_index": 2, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261104, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 63, "truth_numerator": 50, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 15, "unmarked": 13}, "event": "at_least_one_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 0.7936507936507936, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0162", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261105, "batch_index": 2, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261104, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 20, "truth_numerator": 1, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 1, "unmarked": 19}, "B": {"marked": 43, "unmarked": 48}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "A", "selection": "Choose one item uniformly at random from group A only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 0.05, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0163", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261105, "batch_index": 2, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261104, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 182, "truth_numerator": 67, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 5, "B": 5}, "boxes": {"A": {"marked": 4, "unmarked": 9}, "B": {"marked": 3, "unmarked": 4}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.36813186813186816, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0164", "question": "Are both selected items marked?", "source": {"actual_rng_seed": 20261105, "batch_index": 2, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261104, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 145, "truth_numerator": 57, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 19, "unmarked": 11}, "event": "both_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 0.3931034482758621, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0165", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261105, "batch_index": 2, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261104, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 1443, "truth_numerator": 263, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 9, "B": 4}, "boxes": {"A": {"marked": 7, "unmarked": 30}, "B": {"marked": 5, "unmarked": 25}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.18225918225918225, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0166", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261105, "batch_index": 2, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261104, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 1980, "truth_numerator": 631, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 5, "B": 7}, "boxes": {"A": {"marked": 16, "unmarked": 17}, "B": {"marked": 2, "unmarked": 8}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.3186868686868687, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0167", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261105, "batch_index": 2, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261104, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 2, "truth_numerator": 1, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 55, "unmarked": 12}, "B": {"marked": 10, "unmarked": 10}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "B", "selection": "Choose one item uniformly at random from group B only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 0.5, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0168", "question": "Is exactly one of the two selected items marked?", "source": {"actual_rng_seed": 20261105, "batch_index": 2, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261104, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 1, "truth_numerator": 0, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 0, "unmarked": 8}, "event": "exactly_one_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 0.0, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0169", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261105, "batch_index": 2, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261104, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 165, "truth_numerator": 79, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 5, "B": 5}, "boxes": {"A": {"marked": 8, "unmarked": 32}, "B": {"marked": 25, "unmarked": 8}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.47878787878787876, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0170", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261105, "batch_index": 2, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261104, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 247, "truth_numerator": 112, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 9, "B": 4}, "boxes": {"A": {"marked": 4, "unmarked": 15}, "B": {"marked": 18, "unmarked": 0}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.4534412955465587, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0171", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261105, "batch_index": 2, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261104, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 25, "truth_numerator": 19, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 5, "B": 2}, "boxes": {"A": {"marked": 18, "unmarked": 0}, "B": {"marked": 4, "unmarked": 21}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.76, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0172", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261105, "batch_index": 2, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261104, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 60, "truth_numerator": 1, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 1, "unmarked": 59}, "B": {"marked": 6, "unmarked": 33}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "A", "selection": "Choose one item uniformly at random from group A only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 0.016666666666666666, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0173", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261105, "batch_index": 2, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261104, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 3619, "truth_numerator": 1537, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 8, "B": 6}, "boxes": {"A": {"marked": 8, "unmarked": 3}, "B": {"marked": 1, "unmarked": 46}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.42470295661785024, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0174", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261105, "batch_index": 2, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261104, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 85, "truth_numerator": 41, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 1, "B": 9}, "boxes": {"A": {"marked": 11, "unmarked": 23}, "B": {"marked": 10, "unmarked": 10}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.4823529411764706, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0175", "question": "Are both selected items marked?", "source": {"actual_rng_seed": 20261105, "batch_index": 2, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261104, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 378, "truth_numerator": 1, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 2, "unmarked": 26}, "event": "both_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 0.0026455026455026454, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0176", "question": "Are both selected items marked?", "source": {"actual_rng_seed": 20261105, "batch_index": 2, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261104, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 7, "truth_numerator": 5, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 6, "unmarked": 1}, "event": "both_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 0.7142857142857143, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0177", "question": "Is at least one of the two selected items marked?", "source": {"actual_rng_seed": 20261105, "batch_index": 2, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261104, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 55, "truth_numerator": 18, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 8, "unmarked": 37}, "event": "at_least_one_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 0.32727272727272727, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0178", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261106, "batch_index": 3, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261105, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 266, "truth_numerator": 75, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 2, "B": 5}, "boxes": {"A": {"marked": 9, "unmarked": 29}, "B": {"marked": 6, "unmarked": 14}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.2819548872180451, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0179", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261106, "batch_index": 3, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261105, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 2, "truth_numerator": 1, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 5, "unmarked": 14}, "B": {"marked": 30, "unmarked": 30}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "B", "selection": "Choose one item uniformly at random from group B only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 0.5, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0180", "question": "Are both selected items marked?", "source": {"actual_rng_seed": 20261106, "batch_index": 3, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261105, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 5, "truth_numerator": 2, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 4, "unmarked": 2}, "event": "both_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 0.4, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0181", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261106, "batch_index": 3, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261105, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 312, "truth_numerator": 151, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 5, "B": 5}, "boxes": {"A": {"marked": 5, "unmarked": 8}, "B": {"marked": 28, "unmarked": 20}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.483974358974359, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0182", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261106, "batch_index": 3, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261105, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 20, "truth_numerator": 1, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 1, "unmarked": 19}, "B": {"marked": 7, "unmarked": 7}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "A", "selection": "Choose one item uniformly at random from group A only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 0.05, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0183", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261106, "batch_index": 3, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261105, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 40, "truth_numerator": 39, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 39, "unmarked": 1}, "B": {"marked": 3, "unmarked": 7}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "A", "selection": "Choose one item uniformly at random from group A only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 0.975, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0184", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261106, "batch_index": 3, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261105, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 40, "truth_numerator": 21, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 22, "unmarked": 33}, "B": {"marked": 21, "unmarked": 19}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "B", "selection": "Choose one item uniformly at random from group B only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 0.525, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0185", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261106, "batch_index": 3, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261105, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 1, "truth_numerator": 0, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 4, "unmarked": 32}, "B": {"marked": 0, "unmarked": 60}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "B", "selection": "Choose one item uniformly at random from group B only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 0.0, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0186", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261106, "batch_index": 3, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261105, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 27440, "truth_numerator": 12097, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 9, "B": 5}, "boxes": {"A": {"marked": 17, "unmarked": 23}, "B": {"marked": 23, "unmarked": 26}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.4408527696793003, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0187", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261106, "batch_index": 3, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261105, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 20, "truth_numerator": 19, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 19, "unmarked": 1}, "B": {"marked": 1, "unmarked": 12}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "A", "selection": "Choose one item uniformly at random from group A only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 0.95, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0188", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261106, "batch_index": 3, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261105, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 20, "truth_numerator": 11, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 11, "unmarked": 9}, "B": {"marked": 61, "unmarked": 13}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "A", "selection": "Choose one item uniformly at random from group A only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 0.55, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0189", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261106, "batch_index": 3, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261105, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 30, "truth_numerator": 1, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 40, "unmarked": 16}, "B": {"marked": 1, "unmarked": 29}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "B", "selection": "Choose one item uniformly at random from group B only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 0.03333333333333333, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0190", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261106, "batch_index": 3, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261105, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 5, "truth_numerator": 1, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 7, "unmarked": 4}, "B": {"marked": 6, "unmarked": 24}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "B", "selection": "Choose one item uniformly at random from group B only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 0.2, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0191", "question": "Is at least one of the two selected items marked?", "source": {"actual_rng_seed": 20261106, "batch_index": 3, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261105, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 29, "truth_numerator": 21, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 14, "unmarked": 16}, "event": "at_least_one_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 0.7241379310344828, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0192", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261106, "batch_index": 3, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261105, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 414, "truth_numerator": 211, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 3, "B": 3}, "boxes": {"A": {"marked": 6, "unmarked": 40}, "B": {"marked": 40, "unmarked": 5}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.5096618357487923, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0193", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261106, "batch_index": 3, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261105, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 65, "truth_numerator": 22, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 8, "B": 2}, "boxes": {"A": {"marked": 11, "unmarked": 15}, "B": {"marked": 0, "unmarked": 13}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.3384615384615385, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0194", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261106, "batch_index": 3, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261105, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 504, "truth_numerator": 269, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 1, "B": 2}, "boxes": {"A": {"marked": 11, "unmarked": 17}, "B": {"marked": 29, "unmarked": 19}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.5337301587301587, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0195", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261106, "batch_index": 3, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261105, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 40, "truth_numerator": 1, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 1, "unmarked": 39}, "B": {"marked": 19, "unmarked": 12}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "A", "selection": "Choose one item uniformly at random from group A only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 0.025, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0196", "question": "Is exactly one of the two selected items marked?", "source": {"actual_rng_seed": 20261106, "batch_index": 3, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261105, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 66, "truth_numerator": 25, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 25, "unmarked": 8}, "event": "exactly_one_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 0.3787878787878788, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0197", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261106, "batch_index": 3, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261105, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 5, "truth_numerator": 1, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 60, "unmarked": 36}, "B": {"marked": 10, "unmarked": 40}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "B", "selection": "Choose one item uniformly at random from group B only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 0.2, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0198", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261106, "batch_index": 3, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261105, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 1, "truth_numerator": 0, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 11, "unmarked": 9}, "B": {"marked": 0, "unmarked": 50}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "B", "selection": "Choose one item uniformly at random from group B only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 0.0, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0199", "question": "Are both selected items marked?", "source": {"actual_rng_seed": 20261106, "batch_index": 3, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261105, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 21, "truth_numerator": 10, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 5, "unmarked": 2}, "event": "both_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 0.47619047619047616, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0200", "question": "Is at least one of the two selected items marked?", "source": {"actual_rng_seed": 20261106, "batch_index": 3, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261105, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 703, "truth_numerator": 598, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 23, "unmarked": 15}, "event": "at_least_one_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 0.8506401137980085, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0201", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261106, "batch_index": 3, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261105, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 1, "truth_numerator": 0, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 0, "unmarked": 20}, "B": {"marked": 7, "unmarked": 20}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "A", "selection": "Choose one item uniformly at random from group A only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 0.0, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0202", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261106, "batch_index": 3, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261105, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 20, "truth_numerator": 11, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 32, "unmarked": 56}, "B": {"marked": 11, "unmarked": 9}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "B", "selection": "Choose one item uniformly at random from group B only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 0.55, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0203", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261106, "batch_index": 3, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261105, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 2709, "truth_numerator": 1517, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 4, "B": 3}, "boxes": {"A": {"marked": 29, "unmarked": 14}, "B": {"marked": 11, "unmarked": 16}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.5599852344038391, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0204", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261106, "batch_index": 3, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261105, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 75, "truth_numerator": 7, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 9, "B": 9}, "boxes": {"A": {"marked": 3, "unmarked": 22}, "B": {"marked": 1, "unmarked": 14}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.09333333333333334, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0205", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261106, "batch_index": 3, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261105, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 336, "truth_numerator": 251, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 8, "B": 8}, "boxes": {"A": {"marked": 13, "unmarked": 8}, "B": {"marked": 7, "unmarked": 1}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.7470238095238095, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0206", "question": "Is exactly one of the two selected items marked?", "source": {"actual_rng_seed": 20261106, "batch_index": 3, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261105, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 1, "truth_numerator": 0, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 18, "unmarked": 0}, "event": "exactly_one_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 0.0, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0207", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261106, "batch_index": 3, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261105, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 6300, "truth_numerator": 3163, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 2, "B": 8}, "boxes": {"A": {"marked": 23, "unmarked": 5}, "B": {"marked": 19, "unmarked": 26}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.5020634920634921, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0208", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261106, "batch_index": 3, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261105, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 1, "truth_numerator": 1, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 25, "unmarked": 26}, "B": {"marked": 60, "unmarked": 0}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "B", "selection": "Choose one item uniformly at random from group B only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 1.0, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0209", "question": "Is exactly one of the two selected items marked?", "source": {"actual_rng_seed": 20261106, "batch_index": 3, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261105, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 861, "truth_numerator": 416, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 16, "unmarked": 26}, "event": "exactly_one_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 0.4831591173054588, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0210", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261106, "batch_index": 3, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261105, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 1204, "truth_numerator": 631, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 3, "B": 1}, "boxes": {"A": {"marked": 28, "unmarked": 15}, "B": {"marked": 3, "unmarked": 18}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.5240863787375415, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0211", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261106, "batch_index": 3, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261105, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 20, "truth_numerator": 11, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 11, "unmarked": 35}, "B": {"marked": 11, "unmarked": 9}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "B", "selection": "Choose one item uniformly at random from group B only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 0.55, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0212", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261106, "batch_index": 3, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261105, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 264, "truth_numerator": 173, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 9, "B": 3}, "boxes": {"A": {"marked": 26, "unmarked": 10}, "B": {"marked": 10, "unmarked": 12}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.6553030303030303, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0213", "question": "Is at least one of the two selected items marked?", "source": {"actual_rng_seed": 20261106, "batch_index": 3, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261105, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 248, "truth_numerator": 215, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 20, "unmarked": 12}, "event": "at_least_one_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 0.8669354838709677, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0214", "question": "Is exactly one of the two selected items marked?", "source": {"actual_rng_seed": 20261106, "batch_index": 3, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261105, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 22, "truth_numerator": 9, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 24, "unmarked": 9}, "event": "exactly_one_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 0.4090909090909091, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0215", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261106, "batch_index": 3, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261105, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 1, "truth_numerator": 0, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 45, "unmarked": 11}, "B": {"marked": 0, "unmarked": 30}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "B", "selection": "Choose one item uniformly at random from group B only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 0.0, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0216", "question": "Are both selected items marked?", "source": {"actual_rng_seed": 20261106, "batch_index": 3, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261105, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 52, "truth_numerator": 29, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 30, "unmarked": 10}, "event": "both_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 0.5576923076923077, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0217", "question": "Is at least one of the two selected items marked?", "source": {"actual_rng_seed": 20261106, "batch_index": 3, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261105, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 155, "truth_numerator": 78, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 9, "unmarked": 22}, "event": "at_least_one_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 0.5032258064516129, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0218", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261106, "batch_index": 3, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261105, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 770, "truth_numerator": 457, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 6, "B": 5}, "boxes": {"A": {"marked": 9, "unmarked": 19}, "B": {"marked": 23, "unmarked": 2}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.5935064935064935, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0219", "question": "Are both selected items marked?", "source": {"actual_rng_seed": 20261106, "batch_index": 3, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261105, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 190, "truth_numerator": 153, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 18, "unmarked": 2}, "event": "both_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 0.8052631578947368, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0220", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261106, "batch_index": 3, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261105, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 3016, "truth_numerator": 1783, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 2, "B": 6}, "boxes": {"A": {"marked": 5, "unmarked": 24}, "B": {"marked": 19, "unmarked": 7}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.5911803713527851, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0221", "question": "Is exactly one of the two selected items marked?", "source": {"actual_rng_seed": 20261106, "batch_index": 3, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261105, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 18, "truth_numerator": 7, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 7, "unmarked": 21}, "event": "exactly_one_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 0.3888888888888889, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0222", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261106, "batch_index": 3, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261105, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 315, "truth_numerator": 194, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 2, "B": 4}, "boxes": {"A": {"marked": 32, "unmarked": 3}, "B": {"marked": 7, "unmarked": 8}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.6158730158730159, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0223", "question": "Are both selected items marked?", "source": {"actual_rng_seed": 20261106, "batch_index": 3, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261105, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 31, "truth_numerator": 3, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 10, "unmarked": 21}, "event": "both_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 0.0967741935483871, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0224", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261106, "batch_index": 3, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261105, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 372, "truth_numerator": 257, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 8, "B": 4}, "boxes": {"A": {"marked": 14, "unmarked": 2}, "B": {"marked": 10, "unmarked": 21}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.6908602150537635, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0225", "question": "Is exactly one of the two selected items marked?", "source": {"actual_rng_seed": 20261106, "batch_index": 3, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261105, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 25, "truth_numerator": 12, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 16, "unmarked": 9}, "event": "exactly_one_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 0.48, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0226", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261106, "batch_index": 3, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261105, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 1, "truth_numerator": 0, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 0, "unmarked": 60}, "B": {"marked": 28, "unmarked": 33}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "A", "selection": "Choose one item uniformly at random from group A only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 0.0, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0227", "question": "Is exactly one of the two selected items marked?", "source": {"actual_rng_seed": 20261106, "batch_index": 3, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261105, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 253, "truth_numerator": 126, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 14, "unmarked": 9}, "event": "exactly_one_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 0.4980237154150198, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0228", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261106, "batch_index": 3, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261105, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 2, "truth_numerator": 1, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 10, "unmarked": 10}, "B": {"marked": 14, "unmarked": 32}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "A", "selection": "Choose one item uniformly at random from group A only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 0.5, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0229", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261106, "batch_index": 3, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261105, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 47, "truth_numerator": 23, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 4, "B": 4}, "boxes": {"A": {"marked": 46, "unmarked": 1}, "B": {"marked": 0, "unmarked": 48}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.48936170212765956, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0230", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261106, "batch_index": 3, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261105, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 1368, "truth_numerator": 1175, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 5, "B": 7}, "boxes": {"A": {"marked": 17, "unmarked": 2}, "B": {"marked": 25, "unmarked": 5}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.8589181286549707, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0231", "question": "Is at least one of the two selected items marked?", "source": {"actual_rng_seed": 20261106, "batch_index": 3, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261105, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 91, "truth_numerator": 90, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 12, "unmarked": 2}, "event": "at_least_one_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 0.989010989010989, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0232", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261106, "batch_index": 3, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261105, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 161, "truth_numerator": 51, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 5, "B": 2}, "boxes": {"A": {"marked": 1, "unmarked": 4}, "B": {"marked": 14, "unmarked": 9}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.3167701863354037, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0233", "question": "Are both selected items marked?", "source": {"actual_rng_seed": 20261106, "batch_index": 3, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261105, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 1, "truth_numerator": 1, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 11, "unmarked": 0}, "event": "both_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 1.0, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0234", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261106, "batch_index": 3, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261105, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 735, "truth_numerator": 323, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 8, "B": 7}, "boxes": {"A": {"marked": 15, "unmarked": 34}, "B": {"marked": 29, "unmarked": 20}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.43945578231292515, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0235", "question": "Is at least one of the two selected items marked?", "source": {"actual_rng_seed": 20261106, "batch_index": 3, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261105, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 378, "truth_numerator": 53, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 2, "unmarked": 26}, "event": "at_least_one_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 0.1402116402116402, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0236", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261106, "batch_index": 3, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261105, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 50, "truth_numerator": 1, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 29, "unmarked": 38}, "B": {"marked": 1, "unmarked": 49}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "B", "selection": "Choose one item uniformly at random from group B only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 0.02, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0237", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261107, "batch_index": 4, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261106, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 2, "truth_numerator": 1, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 15, "unmarked": 15}, "B": {"marked": 1, "unmarked": 9}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "A", "selection": "Choose one item uniformly at random from group A only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 0.5, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0238", "question": "Are both selected items marked?", "source": {"actual_rng_seed": 20261107, "batch_index": 4, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261106, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 17, "truth_numerator": 15, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 16, "unmarked": 1}, "event": "both_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 0.8823529411764706, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0239", "question": "Is at least one of the two selected items marked?", "source": {"actual_rng_seed": 20261107, "batch_index": 4, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261106, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 1, "truth_numerator": 1, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 11, "unmarked": 1}, "event": "at_least_one_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 1.0, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0240", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261107, "batch_index": 4, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261106, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 1, "truth_numerator": 1, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 20, "unmarked": 0}, "B": {"marked": 65, "unmarked": 28}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "A", "selection": "Choose one item uniformly at random from group A only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 1.0, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0241", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261107, "batch_index": 4, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261106, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 15, "truth_numerator": 8, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 14, "unmarked": 5}, "B": {"marked": 16, "unmarked": 14}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "B", "selection": "Choose one item uniformly at random from group B only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 0.5333333333333333, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0242", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261107, "batch_index": 4, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261106, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 65, "truth_numerator": 16, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 2, "B": 7}, "boxes": {"A": {"marked": 6, "unmarked": 14}, "B": {"marked": 9, "unmarked": 30}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.24615384615384617, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0243", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261107, "batch_index": 4, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261106, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 328, "truth_numerator": 141, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 6, "B": 2}, "boxes": {"A": {"marked": 17, "unmarked": 17}, "B": {"marked": 9, "unmarked": 32}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.4298780487804878, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0244", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261107, "batch_index": 4, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261106, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 1, "truth_numerator": 1, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 40, "unmarked": 0}, "B": {"marked": 21, "unmarked": 12}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "A", "selection": "Choose one item uniformly at random from group A only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 1.0, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0245", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261107, "batch_index": 4, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261106, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 1, "truth_numerator": 1, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 16, "unmarked": 48}, "B": {"marked": 50, "unmarked": 0}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "B", "selection": "Choose one item uniformly at random from group B only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 1.0, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0246", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261107, "batch_index": 4, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261106, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 30, "truth_numerator": 1, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 1, "unmarked": 29}, "B": {"marked": 29, "unmarked": 70}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "A", "selection": "Choose one item uniformly at random from group A only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 0.03333333333333333, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0247", "question": "Are both selected items marked?", "source": {"actual_rng_seed": 20261107, "batch_index": 4, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261106, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 82, "truth_numerator": 19, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 20, "unmarked": 21}, "event": "both_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 0.23170731707317074, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0248", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261107, "batch_index": 4, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261106, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 25, "truth_numerator": 13, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 26, "unmarked": 24}, "B": {"marked": 19, "unmarked": 10}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "A", "selection": "Choose one item uniformly at random from group A only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 0.52, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0249", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261107, "batch_index": 4, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261106, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 1, "truth_numerator": 1, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 30, "unmarked": 0}, "B": {"marked": 13, "unmarked": 4}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "A", "selection": "Choose one item uniformly at random from group A only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 1.0, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0250", "question": "Is exactly one of the two selected items marked?", "source": {"actual_rng_seed": 20261107, "batch_index": 4, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261106, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 205, "truth_numerator": 37, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 37, "unmarked": 4}, "event": "exactly_one_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 0.18048780487804877, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0251", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261107, "batch_index": 4, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261106, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 273, "truth_numerator": 215, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 5, "B": 2}, "boxes": {"A": {"marked": 10, "unmarked": 0}, "B": {"marked": 10, "unmarked": 29}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.7875457875457875, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0252", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261107, "batch_index": 4, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261106, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 1755, "truth_numerator": 1232, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 3, "B": 2}, "boxes": {"A": {"marked": 24, "unmarked": 2}, "B": {"marked": 10, "unmarked": 17}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.701994301994302, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0253", "question": "Is exactly one of the two selected items marked?", "source": {"actual_rng_seed": 20261107, "batch_index": 4, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261106, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 13, "truth_numerator": 6, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 9, "unmarked": 4}, "event": "exactly_one_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 0.46153846153846156, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0254", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261107, "batch_index": 4, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261106, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 1305, "truth_numerator": 566, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 2, "B": 7}, "boxes": {"A": {"marked": 16, "unmarked": 13}, "B": {"marked": 12, "unmarked": 18}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.4337164750957854, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0255", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261107, "batch_index": 4, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261106, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 10440, "truth_numerator": 451, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 7, "B": 1}, "boxes": {"A": {"marked": 2, "unmarked": 43}, "B": {"marked": 1, "unmarked": 28}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.0431992337164751, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0256", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261107, "batch_index": 4, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261106, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 585, "truth_numerator": 283, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 8, "B": 5}, "boxes": {"A": {"marked": 26, "unmarked": 19}, "B": {"marked": 8, "unmarked": 16}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.48376068376068376, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0257", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261107, "batch_index": 4, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261106, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 30, "truth_numerator": 1, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 1, "unmarked": 29}, "B": {"marked": 15, "unmarked": 3}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "A", "selection": "Choose one item uniformly at random from group A only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 0.03333333333333333, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0258", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261107, "batch_index": 4, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261106, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 704, "truth_numerator": 129, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 4, "B": 4}, "boxes": {"A": {"marked": 3, "unmarked": 8}, "B": {"marked": 3, "unmarked": 29}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.18323863636363635, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0259", "question": "Is at least one of the two selected items marked?", "source": {"actual_rng_seed": 20261107, "batch_index": 4, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261106, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 63, "truth_numerator": 44, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 16, "unmarked": 20}, "event": "at_least_one_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 0.6984126984126984, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0260", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261107, "batch_index": 4, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261106, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 5, "truth_numerator": 1, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 42, "unmarked": 48}, "B": {"marked": 12, "unmarked": 48}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "B", "selection": "Choose one item uniformly at random from group B only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 0.2, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0261", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261107, "batch_index": 4, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261106, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 45, "truth_numerator": 19, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 6, "B": 6}, "boxes": {"A": {"marked": 16, "unmarked": 20}, "B": {"marked": 6, "unmarked": 9}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.4222222222222222, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0262", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261107, "batch_index": 4, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261106, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 80, "truth_numerator": 31, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 6, "B": 2}, "boxes": {"A": {"marked": 10, "unmarked": 38}, "B": {"marked": 37, "unmarked": 3}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.3875, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0263", "question": "Is at least one of the two selected items marked?", "source": {"actual_rng_seed": 20261107, "batch_index": 4, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261106, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 117, "truth_numerator": 47, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 6, "unmarked": 21}, "event": "at_least_one_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 0.4017094017094017, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0264", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261107, "batch_index": 4, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261106, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 60, "truth_numerator": 59, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 59, "unmarked": 1}, "B": {"marked": 28, "unmarked": 30}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "A", "selection": "Choose one item uniformly at random from group A only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 0.9833333333333333, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0265", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261107, "batch_index": 4, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261106, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 493, "truth_numerator": 133, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 3, "B": 2}, "boxes": {"A": {"marked": 1, "unmarked": 16}, "B": {"marked": 17, "unmarked": 12}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.2697768762677485, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0266", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261107, "batch_index": 4, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261106, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 30, "truth_numerator": 29, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 29, "unmarked": 1}, "B": {"marked": 39, "unmarked": 48}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "A", "selection": "Choose one item uniformly at random from group A only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 0.9666666666666667, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0267", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261107, "batch_index": 4, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261106, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 60, "truth_numerator": 1, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 1, "unmarked": 59}, "B": {"marked": 43, "unmarked": 3}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "A", "selection": "Choose one item uniformly at random from group A only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 0.016666666666666666, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0268", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261107, "batch_index": 4, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261106, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 275, "truth_numerator": 78, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 7, "B": 8}, "boxes": {"A": {"marked": 8, "unmarked": 12}, "B": {"marked": 2, "unmarked": 9}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.28363636363636363, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0269", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261107, "batch_index": 4, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261106, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 1, "truth_numerator": 0, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 22, "unmarked": 21}, "B": {"marked": 0, "unmarked": 20}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "B", "selection": "Choose one item uniformly at random from group B only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 0.0, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0270", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261107, "batch_index": 4, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261106, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 11, "truth_numerator": 10, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 2, "B": 2}, "boxes": {"A": {"marked": 34, "unmarked": 0}, "B": {"marked": 9, "unmarked": 2}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.9090909090909091, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0271", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261107, "batch_index": 4, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261106, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 5, "truth_numerator": 1, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 8, "unmarked": 32}, "B": {"marked": 0, "unmarked": 46}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "A", "selection": "Choose one item uniformly at random from group A only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 0.2, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0272", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261107, "batch_index": 4, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261106, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 170, "truth_numerator": 141, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 2, "B": 8}, "boxes": {"A": {"marked": 5, "unmarked": 29}, "B": {"marked": 6, "unmarked": 0}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.8294117647058824, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0273", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261107, "batch_index": 4, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261106, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 40, "truth_numerator": 39, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 39, "unmarked": 1}, "B": {"marked": 59, "unmarked": 24}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "A", "selection": "Choose one item uniformly at random from group A only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 0.975, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0274", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261107, "batch_index": 4, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261106, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 1, "truth_numerator": 1, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 50, "unmarked": 0}, "B": {"marked": 83, "unmarked": 7}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "A", "selection": "Choose one item uniformly at random from group A only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 1.0, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0275", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261107, "batch_index": 4, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261106, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 30, "truth_numerator": 29, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 17, "unmarked": 2}, "B": {"marked": 29, "unmarked": 1}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "B", "selection": "Choose one item uniformly at random from group B only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 0.9666666666666667, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0276", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261107, "batch_index": 4, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261106, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 440, "truth_numerator": 123, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 6, "B": 5}, "boxes": {"A": {"marked": 1, "unmarked": 4}, "B": {"marked": 6, "unmarked": 10}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.27954545454545454, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0277", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261107, "batch_index": 4, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261106, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 600, "truth_numerator": 397, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 7, "B": 3}, "boxes": {"A": {"marked": 16, "unmarked": 8}, "B": {"marked": 13, "unmarked": 7}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.6616666666666666, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0278", "question": "Is at least one of the two selected items marked?", "source": {"actual_rng_seed": 20261107, "batch_index": 4, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261106, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 39, "truth_numerator": 2, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 1, "unmarked": 38}, "event": "at_least_one_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 0.05128205128205128, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0279", "question": "Is exactly one of the two selected items marked?", "source": {"actual_rng_seed": 20261107, "batch_index": 4, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261106, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 31, "truth_numerator": 7, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 28, "unmarked": 4}, "event": "exactly_one_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 0.22580645161290322, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0280", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261107, "batch_index": 4, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261106, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 54, "truth_numerator": 41, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 5, "B": 4}, "boxes": {"A": {"marked": 6, "unmarked": 3}, "B": {"marked": 21, "unmarked": 3}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.7592592592592593, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0281", "question": "Is exactly one of the two selected items marked?", "source": {"actual_rng_seed": 20261107, "batch_index": 4, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261106, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 1, "truth_numerator": 0, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 0, "unmarked": 10}, "event": "exactly_one_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 0.0, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0282", "question": "Are both selected items marked?", "source": {"actual_rng_seed": 20261107, "batch_index": 4, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261106, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 946, "truth_numerator": 741, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 39, "unmarked": 5}, "event": "both_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 0.7832980972515856, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0283", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261107, "batch_index": 4, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261106, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 13079, "truth_numerator": 6152, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 9, "B": 2}, "boxes": {"A": {"marked": 14, "unmarked": 15}, "B": {"marked": 17, "unmarked": 24}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.4703723526263476, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0284", "question": "Is at least one of the two selected items marked?", "source": {"actual_rng_seed": 20261107, "batch_index": 4, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261106, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 276, "truth_numerator": 185, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 10, "unmarked": 14}, "event": "at_least_one_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 0.6702898550724637, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0285", "question": "Is at least one of the two selected items marked?", "source": {"actual_rng_seed": 20261107, "batch_index": 4, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261106, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 153, "truth_numerator": 143, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 13, "unmarked": 5}, "event": "at_least_one_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 0.934640522875817, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0286", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261107, "batch_index": 4, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261106, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 805, "truth_numerator": 561, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 4, "B": 6}, "boxes": {"A": {"marked": 22, "unmarked": 1}, "B": {"marked": 11, "unmarked": 10}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.6968944099378882, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0287", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261107, "batch_index": 4, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261106, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 60, "truth_numerator": 31, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 14, "unmarked": 8}, "B": {"marked": 31, "unmarked": 29}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "B", "selection": "Choose one item uniformly at random from group B only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 0.5166666666666667, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0288", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261107, "batch_index": 4, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "weighted_mixture", "seed": 20261106, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 1722, "truth_numerator": 1609, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"box_selection_tickets": {"A": 6, "B": 1}, "boxes": {"A": {"marked": 39, "unmarked": 2}, "B": {"marked": 5, "unmarked": 1}}, "interpretation": "Estimate the probability of the event for this random item, accounting for both stages of selection.", "selection": "First choose one ticket uniformly at random from all tickets. The ticket names box A or box B. Then choose one item uniformly at random from that box. There is no further information about the chosen box.", "setting": "Two fictional boxes contain complete populations. Their contents are listed below."}, "target": 0.9343786295005807, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0289", "question": "Are both selected items marked?", "source": {"actual_rng_seed": 20261107, "batch_index": 4, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261106, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 301, "truth_numerator": 2, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 4, "unmarked": 39}, "event": "both_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 0.006644518272425249, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0290", "question": "Are both selected items marked?", "source": {"actual_rng_seed": 20261107, "batch_index": 4, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261106, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 23, "truth_numerator": 10, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 16, "unmarked": 8}, "event": "both_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 0.43478260869565216, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0291", "question": "Is exactly one of the two selected items marked?", "source": {"actual_rng_seed": 20261107, "batch_index": 4, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261106, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 7, "truth_numerator": 2, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 6, "unmarked": 1}, "event": "exactly_one_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 0.2857142857142857, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0292", "question": "Is the selected item marked?", "source": {"actual_rng_seed": 20261107, "batch_index": 4, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "conditional_table", "seed": 20261106, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 20, "truth_numerator": 1, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"A": {"marked": 1, "unmarked": 19}, "B": {"marked": 25, "unmarked": 12}}, "interpretation": "Estimate the probability of the event for this one random draw, using the supplied counts.", "selected_group": "A", "selection": "Choose one item uniformly at random from group A only.", "setting": "Fictional inventory. The following table describes the entire population, not a sample."}, "target": 0.05, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0293", "question": "Is exactly one of the two selected items marked?", "source": {"actual_rng_seed": 20261107, "batch_index": 4, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261106, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 1, "truth_numerator": 0, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 0, "unmarked": 41}, "event": "exactly_one_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 0.0, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0294", "question": "Are both selected items marked?", "source": {"actual_rng_seed": 20261107, "batch_index": 4, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261106, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 301, "truth_numerator": 247, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 39, "unmarked": 4}, "event": "both_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 0.8205980066445183, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0295", "question": "Are both selected items marked?", "source": {"actual_rng_seed": 20261108, "batch_index": 5, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261107, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 155, "truth_numerator": 2, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 4, "unmarked": 27}, "event": "both_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 0.012903225806451613, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0296", "question": "Is at least one of the two selected items marked?", "source": {"actual_rng_seed": 20261108, "batch_index": 5, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261107, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 60, "truth_numerator": 49, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 14, "unmarked": 11}, "event": "at_least_one_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 0.8166666666666667, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0297", "question": "Is at least one of the two selected items marked?", "source": {"actual_rng_seed": 20261108, "batch_index": 5, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261107, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 247, "truth_numerator": 147, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 14, "unmarked": 25}, "event": "at_least_one_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 0.5951417004048583, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0298", "question": "Is at least one of the two selected items marked?", "source": {"actual_rng_seed": 20261108, "batch_index": 5, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261107, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 22, "truth_numerator": 1, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 1, "unmarked": 43}, "event": "at_least_one_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 0.045454545454545456, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0299", "question": "Is exactly one of the two selected items marked?", "source": {"actual_rng_seed": 20261108, "batch_index": 5, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261107, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 25, "truth_numerator": 7, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 21, "unmarked": 4}, "event": "exactly_one_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 0.28, "target_kind": "probability"}
{"criteria": {"false": "The stated event does not occur in that random selection.", "true": "The stated event occurs in the random selection described in the state."}, "experiment": "probability", "id": "expanded-probability-0300", "question": "Is at least one of the two selected items marked?", "source": {"actual_rng_seed": 20261108, "batch_index": 5, "generator": "expanded/datasets.py using pinned pilot probability generator", "generator_version": 1, "kind": "synthetic_exact_probability", "pilot_overlap": false, "probability_family": "without_replacement", "seed": 20261107, "selection": "Keep first unique generated problems until 100 per family; exclude pilot-identical inputs.", "shared_pilot_templates": true, "truth_denominator": 301, "truth_numerator": 300, "validation": "Exact rational probability from the complete population and stated random selection mechanism"}, "state": {"counts": {"marked": 40, "unmarked": 3}, "event": "at_least_one_marked", "interpretation": "Estimate the probability of the event for these two random draws, using the supplied counts.", "selection": "Select two different items uniformly at random without replacement. Every unordered pair is equally likely.", "setting": "A fictional box contains the entire population described by these counts."}, "target": 0.9966777408637874, "target_kind": "probability"}