Starting at 7 am, buses arrive at a particular bus stop in a college campus at intervals of 15 minutes (that is, at 7 am, 7:15, 7:30, etc.). Joe is a frequent passenger on this route, and the time he arrives each morning to catch a bus is known to be uniformly distributed between 7 am and 7:30 am.
a. What is the probability that Joe waits less than 5 minutes for a bus?
b. What is the probability that he waits more than 10 minutes for a bus?