A long wait for the bus

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Buses arrive at a stop exactly every 15 minutes. You show up at a uniformly random time. What is the probability you wait more than 9 minutes for the next bus?

Accepted Answer

Your wait is uniform on [0, 15] minutes. A wait over 9 minutes covers the interval (9, 15], of length 15 - 9 = 6: P(	ext{wait} 9) = \frac{6}{15} = \frac25 . Takeaway. "Wait more than t" is the tail length T - t over T. Here 	frac{15 - 9}{15} = 	frac25.

A long wait for the bus

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