Bertrand's Chord
A chord of a circle is drawn by choosing its two endpoints independently and uniformly on the circumference. What is the probability the chord is longer than a side of the inscribed equilateral triangle? Express as a fraction.
Related problems & prerequisites
Worth solving first
- All in a Semicircle 6.0/10
- The Broken Stick 5.0/10
- Ant on a Cube 5.0/10
Source: Bertrand's paradox, from Joseph Bertrand, 'Calcul des probabilites' (1889). Statement written for AxiomIQ.