Solution
The Rendezvous
Show the problem again
Two friends agree to meet between noon and 1 pm. Each arrives at a uniformly random time and waits exactly 15 minutes before leaving (or until 1 pm, whichever comes first). What is the probability they meet? Express as a fraction.
Worked solution
The answer is 7/16. Model arrival times (x, y) as a point in a 60 × 60 square; they meet iff |x − y| ≤ 15. The complement consists of two right triangles with legs 45, total area 2 × (45²/2) = 2025. So P(meet) = 1 − 2025/3600 = 7/16.
Source: Classic uniform-meeting-time problem from geometric probability. Statement written for AxiomIQ.