Socially Distanced Points
Three points are chosen independently and uniformly at random on the interval [0, 1]. What is the probability that every two of them are at least 1/4 apart? 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.