Two automated testing machines work together testing circuit boards. Each one is independently subject to failure. The failure rate of an automated testing machine, when it is in use, is 0.01 per...

Two automated testing machines work together testing circuit boards. Each one is independently subject to failure. The failure rate of an automated testing machine, when it is in use, is 0.01 per hour, with the actual time to failure being exponentially distributed. The time required to repair an automated testing machine is also exponentially distributed with mean 24 hours, and only one machine can be repaired at a time. When one of the automated testing machines has failed, the other handles all of the work, which increases its failure rate to 0.02 per hour.

(a) What is the long-run fraction of the time that both testing machines are not working?

(b) What is the long-run fraction of time that at least one testing machine is not working?