A limousine service catering to a large metropolitan area has found that the time for a trip (from dispatch to return) is exponentially distributed with a mean of 30 minutes.
(a) What is the probability that a trip will take more than an hour?
(b) If a limousine has already been gone for 45 minutes, what is the probability that it will return within the next 20 minutes?
(c) If two limousines have just been dispatched, what is the probability that both will not return within the next 45 minutes? Assume that the trips are independent of each other.