12. The life, in years, of a certain type of electrical switch has an exponential distribution with an average lifetime of 2 years. (a) (3 points) If 100 of these switches are installed in different systems, what is the probability that at most 30 fail during the rst year? (b) (3 points) For a single system, what is the probability we can keep the switching mechanism operable for 10 years if we assume we will have to replace a switch due to failures three times during the 10-year period