7.9 A machine has four identical components that fail independently. When a component is operational, the time until it fails is exponentially distributed with a mean of 10 h. There is one resident repairman at the site so that when a component fails, the repairman immediately swaps it out and commences servicing it to bring it back to the operational state. When the repairman has finished repairing a failed component, the repairman immediately swaps it back into the machine. The time to service each failed component is exponentially distributed with a mean of 2 h. Assume the machine needs at least two operational components to work.

a. What is the probability that only one component is working?

b. What is the probability that the machine is down?