Three for Coffee
Three friends each arrive at a cafe at an independent, uniformly random time between 12:00 and 13:00. Each stays for exactly 15 minutes after arriving (the cafe stays open as long as needed) and then leaves. What is the probability that at some moment all three are in the cafe at the same time? Give a reduced fraction.
Related problems & prerequisites
Worth solving first
- Coin on the Tiles 6.0/10
- Nearest Wall of a Triangle 6.0/10
- The Broken Stick 5.0/10
Source: Classic geometric-probability exercise in wide circulation; no traceable original source. Statement written for AxiomIQ.