Sell the film for $1.

(a) If the six states of nature correspond to 0, 1, 2, 3, 4, and 5 defective sheets in the package, complete the following payoff table:

These data indicate that each state of nature is equally likely, so that this prior distribution can be assumed. What is the optimal action under Bayes’ decision rule (before the attached sheet is tested)
for a package of film?

(c) Now assume that the attached sheet is tested. Use a probability tree diagram to find the posterior probabilities of the state of nature for each of the two possible outcomes of this testing.
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(d) What is the optimal expected payoff for a package of film if the attached sheet is tested? What is the optimal action if the sheet is good? If it is bad?