5. (20 pts) Amy and Charles are at a bus stop. There are two busses, B1 and B2, that stop at this station, and each person takes Whichever bus that comes rst. The buses B1 and B2, reSpectively, arrive in accordance With independent Poisson processes With rates 1 per 15 minutes and 1 per 10 minutes. Assume that Amy and Charles wait for a bus for independently and exponentially distributed amount of times X and Y, With respective means 15 and 20 minutes, then they give up and go back home, indepen- denlty of each other, if any bus still has not come that time. Let T1 and T2 denote the rst interarrival times of the busses B1 and B2, respectively. Assume that X, Y, T1 and T2 are independent. What is the probability that no one takes the bus