Continuing Exercise 29, suppose now that before making a decision on whether to check the production process, two parts are made and examined.

(a) If, in fact, repair is not needed, what are the probabilities that both parts, just one part. and neither part will fail to meet specifications?

(b) Compute the same probabilities as in part (a), given that repair of the production process is in fact needed.

(c) Compute the posterior probabilities of the states of nature and determine the optimal action under the expected monetary value criterion, given each of the following cir- cumstances: (i) Both parts fail to meet specifications. (ii) Just one part fails to meet specifications. (iii) Neither part fails to meet specifications.