(Solution) - Consider again the conditions of Exercise 14 in Sec 2 1 -(2025 Original AI-Free Solution)

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Consider again the conditions of Exercise 14 in Sec. 2.1. Suppose that several parts will be observed and that the different parts are conditionally independent given each of the three states of repair of the machine. If seven parts are observed and exactly one is defective, compute the posterior probabilities of the three states of repair.