The Paradox Portal
Mathematical

Bertrand's Paradox

What's the probability a random chord is longer than the triangle side?

Overview

A probability paradox showing that 'random' can have multiple interpretations leading to different answers.

What's the probability a random chord in a circle is longer than the side of an inscribed equilateral triangle? Different methods of randomly choosing chords give different answers: 1/2, 1/3, or 1/4. Which is correct?

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