Question

You arrive at a bus stop at 10:00. You know that the bus will arrive sometime between 10:00 and 10:30, and you believe that the arrival time is distributed uniformly in this interval. (a) What is the probability you have to wait more than 10 minutes?

Answer 1

2/3 or 0.667

Explanation:

Since the bus arrival time is distributed uniformly in the interval from 10:00 and 10:30, 30 minutes. The probability that you will have to wait more than 10 minutes is 1 minus the probability you will have to wait 10 minutes or less. And since it's a distribution uniform, that probability is 10/30 = 1/3. So in the end, the probability that you will have to wait for more than 10 minutes is 1 - 1/3 = 2/3 or 0.667