{
  "example_kind": "original synthetic manual planning case",
  "slug": "serial-gate-probability-assumptions",
  "title": "Inspect a toy probability across serial gates",
  "scenario": "Synthetic planning case: A toy model requires two gates to pass. Supplied probabilities are 0.9 for A and 0.8 for B. One proposal multiplies them without stating whether the events are independent.",
  "layout": "evaluation",
  "dataset": {
    "heading": "Inspect the invented case records",
    "headers": [
      "Event",
      "Supplied probability",
      "Condition"
    ],
    "rows": [
      [
        "A passes",
        "0.9",
        "Marginal only"
      ],
      [
        "B passes",
        "0.8",
        "Marginal only"
      ],
      [
        "Both pass",
        "0.72",
        "If independent"
      ]
    ]
  },
  "derivation": "Under independence, P(A and B)=0.9×0.8=0.72. With these marginals, joint probability could instead lie between max(0,0.9+0.8−1)=0.7 and min(0.9,0.8)=0.8. The multiplication chooses one dependence model.",
  "result": "The joint pass probability is 0.72 only under the supplied independence assumption. Without a joint model, the two marginal probabilities alone do not identify that result.",
  "boundary": "This distinguishes a joint requirement from marginal probability inputs and makes independence inspectable.",
  "limitations": "No real gate probabilities or deadline confidence have been validated. The bounds describe this two-event mathematical model only.",
  "sources": [
    "original"
  ],
  "tasks": [
    [
      "Define the joint requirement",
      "Planning owner",
      "Both gates, rather than either gate, are required in this model."
    ],
    [
      "Expose dependence assumptions",
      "Method reviewer",
      "Shared inputs or reviewers are considered before assuming independent events."
    ],
    [
      "Bound the probability claim",
      "Decision owner",
      "The note names the conditional model and does not call 72% a validated deadline forecast."
    ]
  ],
  "faqs": [
    [
      "Can two different owners make events independent?",
      "No. Shared work, inputs and circumstances can still connect their outcomes."
    ],
    [
      "Are the supplied probabilities measured?",
      "No. They are invented model inputs; the example demonstrates conditional arithmetic."
    ]
  ],
  "method_references": [
    {
      "id": "original",
      "title": "Original worked-case definitions",
      "scope": "Definitions, policy choices, records and calculations are authored for this worksheet. No external standard, statistical validation or live product measurement is claimed."
    }
  ]
}