A machine can either be in excellent, good, fair, or poor working condition at each time. Given that its current condition is any of the first three, it can be in either the same condition next time with probability .95 , or in a condition that is one level worse with the remaining probability. When the machine reaches the poor condition, it stays there. At least how much time must elapse before a machine that begins in excellent condition reaches poor condition with probability at least \(1 / 2\) ?