Alice has two identical personal computers, which she never uses at the same time. She uses one PC at a time and the other is a backup. If the one she is currently using fails, she turns it off, calls the PC repairman and turns on the backup PC. The time until either PC fails when it is in use is exponentially distributed with a mean of 50 hours. The time between the moment a PC fails until the repairman comes and finishes repairing it is also exponentially distributed with a mean of 3 hours. What is the probability that Alice is idle because neither PC is operational?