Two random arrivals, a one-hour window, and only fifteen minutes of waiting. The answer is hidden inside a square.
The Fifteen-Minute Meeting
Riddle statement
Two friends agree to meet between 6:00 and 7:00. Each arrives independently of the other, at a time chosen uniformly at random during that hour.
Whoever arrives first waits for 15 minutes. If the other friend does not appear during that time, the first one leaves.
Which is more likely: that they meet or that they miss each other? What is the exact probability that they meet?