All in a Semicircle
Three points are chosen independently and uniformly at random on a circle. What is the probability that all three lie within some semicircle? Express as a fraction.
Related problems & prerequisites
Worth solving first
- The Broken Stick 5.0/10
- The Rendezvous 5.0/10
- Buffon's Needle 5.0/10
Source: Classic geometric-probability exercise found in standard probability texts; no single originator. Statement written for AxiomIQ.