The power failures in a certain region occur according to a Poisson pro- cess with rate A, = 1/5 per week. Moreover, the duration X (in hours) of a given power failure has an exponentinl distribution with parameter d2 = 1/2. Finally, we assume that the durations of the various power failures are inde- pendent random variables. (a) What is the probability that the longest failure, among the first threc power failures observed, lasts more than four hours? (b) Suppose thant there has been exactly one power failuro during the first week considered. What is the probability that the failure hnd still not been

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