Cognitive Scaffold

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MENTAL MODEL · M7512

Bertrand Paradox

Bertrand Paradox
TechnicalHigh supportProbability Theory
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Version 1.0.0 · Updated 2026-07-30

CORE DEFINITION

Bertrand Paradox: The same problem ("the probability that a random chord in a circle is longer than the side of an inscribed equilateral triangle") can yield different answers (1/2, 1/3, 1/4) depending on how "random" is defined.

SCAFFOLDING EFFECT

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Reduce cognitive load

A warning for conceptual precision. It reminds us that "random" is not a self-evident concept; the random mechanism must be clearly defined, otherwise the problem itself is incomplete.

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Anchor fast decisions

The same problem (the probability that a random chord in a circle is longer than the side of an inscribed equilateral triangle) yields three solutions (1/2, 1/3, 1/4) depending on how "random" is defined. This shows that "random" is not self-evident; the random mechanism must be clearly defined, otherwise the problem is incomplete.

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Source support: Explicit

  • link
    en.wikipedia.orghttps://en.wikipedia.org/wiki/Bertrand%27s_paradoxZH · Explicit
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