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5. A system consisting of n components is said to be a k-out-of-n system (ksn) if the system functions during a given mission time if and only if at least k of the n components function. Suppose that all components function independently of each other. a) If the ith component functions with probability P, i-1,2,3 derive the formula for the probability that a 2-out-of-3 system functions. b) Repeat part a) for a 3-out-of-4 system. c) Calculate the probability that the system in 5a) functions when P, -0.9 for i-1,2,3, and also in 5b) when P, -0.8 for i-1,2,3,4. Which system is more reliable and why?

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