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Question

A and B are friends. They decide to meet between 1 PM and 2 PM on a given day. There is a condition that whoever arrives first will not wait for the other for more than 15 minutes. The probability that they will meet on that day is

Assume independent arrival times, each uniform from1 p.m. to2 p.m.

The correct answer is

7/16

Meeting requires arrival times within15 minutes. In the60×60 minute square, the two excluded triangles have total area45². Hence probability is1−45²/60²=7/16.

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