The length of time until the breakdown of an essential piece of equipment is important in the decision of the use of auxiliary equipment. Assume time to breakdown of a randomly chosen generator, Y, follows an exponential distribution with a mean of 15 days.
(a) What is the probability a generator will break down in the next 21 days?
(b) A company owns 7 such generators. Let X denote the random variable describing how many generators break down in the next 21 days. Assuming the breakdown of any one generator is independent of breakdowns of the other generators, what is the probability that at least 6 of the 7 generators will operate for the next 21 days without a breakdown?