Suppose you are at Central Campus Transit Center (CCTC), and two bus routes will take you from central to north campus. Assume each route has only one bus running, but both are not there when you arrive at CCTC. You plan to get on the first bus that comes. Let the time it takes bus 1 to return to CCTC be exponentially distributed with rate 1, and the time it takes bus 2 to return to CCTC be exponentially distributed with rate 2. Since the time you got to CCTC, what is the probability that the first bus to eventually pick you up will again return to CCTC before the other bus reaches CCTC for the first time? Hint: One bus has to visit CCTC twice before the other