Two traders trying to meet

Question

Two traders each arrive at the desk at a uniformly random time between 9:00 and 10:00, independently of each other. Whoever arrives first waits 15 minutes for the other before leaving.

What is the probability that they actually meet?

Accepted Answer

Let each arrival be a fraction of the 60-minute window, so both arrival times are uniform on a 0-to-60 scale. Picture the pair of arrival times as a single point (x, y) dropped uniformly into a 60-by-60 square. Every outcome is one point, and all points are equally likely, so probabilities become areas: favorable area divided by total area. They meet exactly when their arrival times are within 15 minutes of each other: x - y \le 15. This is a diagonal band through the square. It is easier to find the area they do not meet, the two corner triangles where x - y 15. Each triangle has legs of len…

Two traders trying to meet

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