Question

Alice takes the bus to school. The bus is scheduled to arrive at a bus stop at 9:30am. In reality, the time the bus arrives is uniformly distributed between 9:28am and 9:40am. Let ? be the number of minutes it takes, starting from 9:28 am, for the bus to arrive to the bus stop. Then ? is uniformly distributed between 0 and 12 minutes.
(a) If Alice arrives at the bus stop at exactly 9:33 am, what is the probability that she missed the bus?
(b) Alice arrives at 9:33 am, and someone who has been at the bus stop says they have been there since 9:25am and the bus has not yet arrived. What is the probability that Alice will wait less than 5 minutes for the bus?
(c) If Alice arrives at 9:33 am, should she expect to miss the bus?

Answer 1