Cognitive Scaffold

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MENTAL MODEL · M7691

Total Probability Theorem

Total Probability Theorem
TechnicalHigh supportProbability Theory
Included
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Version 1.0.0 · Updated 2026-07-30

CORE DEFINITION

If event B can be partitioned into mutually exclusive and exhaustive sub-events {A₁, A₂, ...Aₙ}, then P(B) = Σ P(Aᵢ)·P(B|Aᵢ) — calculating the total probability by enumerating all possible paths.

SCAFFOLDING EFFECT

psychology

Reduce cognitive load

No omission analysis, complete reasoning. Forces consideration of "all possible paths" to avoid missing low-probability but high-impact possibilities. (Merged: Total Probability Formula, Total Probability Model)

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Anchor fast decisions

Decompose event B using a mutually exclusive and exhaustive partition {Aᵢ}, P(B)=ΣP(Aᵢ)P(B|Aᵢ). By enumerating all paths (cause → effect) to find the total probability, it forces inclusion of low-probability high-impact paths.

MINIMUM ACTION

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Source support: Explicit

  • link
    zh.wikipedia.orghttps://zh.wikipedia.org/wiki/%E5%85%A8%E6%A9%9F%E7%8E%87%E5%AE%9A%E7%90%86ZH · Explicit
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