Question: A system consists of five components in two branches as shown in the following diagram:In other words, the system works if components A and B

A system consists of five components in two branches as shown in the following diagram:In other words, the system works if components A and B work or components C, D, and E work. Assume that the components fail independently with the following probabilities:P(A fails) = P(B fails) = 0.3 and P(C fails) = P(D fails) = P(E fails) = 0.2.(a) What is the probability that the system works? (b) Given that component A works, what is the probability that the system does not work? (c) Given the system does not work, what is the probability that component C also does not work?

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