Question: The bus company from Blissville decides to start service in Blotchville, sensing a promising business opportunity. Meanwhile, Fred has moved back to Blotchville. Now when Fred arrives at the bus stop, either of two independent bus lines may come by (both of which take him home). The Blissville company's bus arrival times are exactly 10 minutes apart, whereas the time from one Blotchville company bus to the next is Expo(1/10). Fred arrives at a uniformly random time on a certain day.
(a) What is the probability that the Blotchville company bus arrives first? Hint: One good way is to use the continuous law of total probability.
(b) What is the CDF of Fred's waiting time for a bus?