Buses arrive at a certain stop every 15 min starting at 7 a.m. A passenger arrives at the stop at a time that is uniformly distributed between 7:00 a.m. and 7:30 a.m. (X refers to the number of minutes past 7 a.m., and X is uniformly distributed over the interval (0, 30)).
a) Find the probability that he waits less than 2 min for a bus.
b) Find the probability that he waits more than 10 min for a bus.