Let X denote the lifetime of a radio, in years, manufactured by a certain company. Assume that X is exponentially distributed, with a mean of 5 years.
(a) What is the probability that a radio will work for 10 years?
(b) Sam decides to purchase another 10 radios of this type. What is the exact probability that, of 10 such radios that Sam purchases, at least one of them will last more than 15 years?
(c) Among the 10 radios that Sam purchases, how many radios are expected to last more than 15 years?