Waiting in a middle band for the shuttle

Question

A shuttle leaves a terminal exactly every 20 minutes. You arrive at a uniformly random time. What is the probability you wait between 5 and 15 minutes for the next shuttle?

Accepted Answer

Your wait is uniform on [0, 20] minutes. A wait in the band [5, 15] has length 15 - 5 = 10: P(5 \le 	ext{wait} \le 15) = \frac{10}{20} = \frac12 . Takeaway. A wait falling in an interval [a, b] has probability 	frac{b - a}{T}. The middle half of the cycle here is exactly a coin flip.

Waiting in a middle band for the shuttle

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