Two people agree to meet at a coffee shop. They each independently pick a random moment in time between 8 a.m. and 9 a.m. and show up exactly at their selected time. But they are very impatient, and only stay for 10 minutes after when they arrive. What is the probability that they meet? Express your answer as a common fraction.

3 answers

If person A shows up between 8:10 and 8:50, the probability of their meeting is 1/3, because person B can show up as much as ten minutes earlier or later. The probability of meeting decreases to 1/6 if person A shows up at exactly 8 or 9 AM. The situation between 8:00 and 8:10 and between 8:50 and 9:00 is a bit more complex. I suggest. you work it out.

11/36