The Arc Through the North Pole
A circle has circumference 1. Three points are chosen independently and uniformly at random on it, dividing it into three arcs. A fixed point N (the "north pole") lies on one of these arcs (with probability 1, not at an endpoint). What is the expected length of the arc that contains N? Give a reduced fraction.
Related problems & prerequisites
Worth solving first
- Two Marks on a Ruler 5.0/10
- A Triangle on the Circle 3.0/10
Source: Classic geometric-probability exercise in wide circulation; no traceable original source. Statement written for AxiomIQ.