consider two machines that are maintained by a single repairman. ma- chine 1 functions for an exponential amount of time with rate 1 before it fails and machine 2 functions for an exponential amount of time with rate 3 before it fails. the repair times are exponentially distributed with rates 2 and 5, respectively. the machines are repaired in the order they fail. what is the long run probability that both machines are working?