A.4 An engineering system consisting of n components in parallel working is said to be a k-out- of-n system, that is, the system functions well if and only if at least k components from the total n components operate normally without any failure. Suppose all the components works independently of each other. a) b) For a 4-out-of-5 system, assume each component independently works with different probability. The probability of ith component in normal working condition is assumed to be P, = E, i = 1,2, ,5, for example, the lSt component (i = 1) has the probability of g to operate normally. Compute the probability that the 4-out-of-5 system could operate. For a 2-out-of-4 system, assume each component independently works and follows an exponential distribution. The mean time to failure of each components is 5 hours. if we know the 2-out-of-4 system function well after 4 hours, what is the probability that all the 4 components could work in normal condition aer 4 hours