A system consists of five components is connected in series as shown below. As soon as one component fails, the entire system will fail. Assume that the components fail independently one another. (a) Suppose that each of the first two components have lifetimes that are exponentially distributed with mean weeks, and that each of the last three components have lifetimes that are exponentially distributed with me 126 weeks. Find the probability that the system lasts at least 57 weeks. (b) Now suppose that each component has a lifetime that is exponentially distributed with the same mean. Wh must that mean be (in years) so that 86% of all such systems lasts at least one year?

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