A brewery utilizes two bottling machines, but they do not operate simultaneously. The second machine acts as a backup system to the first machine and operates only when the first breaks down during operating hours. The probability that the first machine breaks down during operating hours is .20. If, in fact, the first breaks down, then the second machine is turned on and has a probability of .30 of breaking down.
a. What is the probability that the brewery’s bottling system is not working during operating hours?
b. The reliability of the bottling process is the probability that the system is working during operating hours. Find the reliability of the bottling process at the brewery.