answer all questions with explanation

1.2. A machine has two vital components: component A and component B. The machine stops working if either one of the components breaks down. The lifetime of component A is an exponential r.v. with a mean of 10 hours. The lifetime of component B is an exponential r.v. with a mean of 1 hour. Suppose that both components are working at the start of the day. (i) What is the expected time (in hours) until the machine stops working? (ii) What is the probability that component A is the rst to break down? (iii) We are told that the machine stopped after 30 minutes. Given this information, what is the probability that component A was the rst to break down? (iv) We are told that the machine stopped working after 20 hours Given this information, what is the probability that component A was the rst to break down