Two diners arriving within ten minutes of each other

Question

Two friends agree to meet at a restaurant. Each turns up at an independent, uniformly random time between 8:00 pm and 9:00 pm, waits exactly $10$ minutes, and leaves if the other has not appeared. What is the probability that they meet?

Short answer

$\tfrac{11}{36}$ . Measuring arrival times in minutes after 8:00, the pair is uniform on a $60\times60$ square and they meet when the times differ by at most 10. The complement is two triangles of total area $50^2$ , so the probability is $\tfrac{3600-2500}{3600}=\tfrac{11}{36}$ .

Adapted from QuantQuestions.io; question and answer rewritten by SelfMadeQuant.com.

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