{
  "label": "Synthetic arithmetic examples, not observed learner data or an FSRS forecast.",
  "assumptions": "Independent binary attempts with the same fixed p=0.9; counts are exact-model 5th and 95th percentile endpoints, not confidence intervals. Discreteness makes inclusive coverage exceed 90%.",
  "probability_method": "Binomial formula evaluated with Decimal precision 70; no RNG or seed.",
  "rows": [
    {
      "attempts": 20,
      "assumed_p": 0.9,
      "lower_count": 16,
      "upper_count": 20,
      "lower_percent": 80.0,
      "upper_percent": 100.0,
      "range_probability": 0.9568255047155366,
      "perfect_session_probability": 0.1215766545905693,
      "sd_percentage_points": 6.708203932499369
    },
    {
      "attempts": 100,
      "assumed_p": 0.9,
      "lower_count": 85,
      "upper_count": 95,
      "lower_percent": 85.0,
      "upper_percent": 95.0,
      "range_probability": 0.9363983902254399,
      "perfect_session_probability": 2.6561398887587476e-5,
      "sd_percentage_points": 3.0
    },
    {
      "attempts": 1000,
      "assumed_p": 0.9,
      "lower_count": 884,
      "upper_count": 915,
      "lower_percent": 88.4,
      "upper_percent": 91.5,
      "range_probability": 0.9081536018628305,
      "perfect_session_probability": 1.7478712517226515e-46,
      "sd_percentage_points": 0.9486832980505138
    }
  ],
  "denominator_example": {
    "distinct_cards": 20,
    "all_attempts": 40,
    "all_passes": 38,
    "all_attempt_pass_percent": 95,
    "first_attempts": 20,
    "first_passes": 18,
    "first_attempt_pass_percent": 90
  },
  "checks": [
    "probability sums",
    "binomial mean and variance identities",
    "two fair trials control",
    "perfect-session identity",
    "synthetic-log accounting"
  ]
}