A machine shop owner is attempting to decide whether to purchase a new drill press, a lathe, or a grinder. The return from each will be determined by whether the company succeeds in getting a government military contract. The profit or loss from each purchase and the probabilities associated with each contract outcome are shown in the following payoff table:

Purchase Contract(0.4) No Contract(0.6)

Drill press $40,000 $-8,000

Lathe $20,000 $4,000

Grinder $12,000 $10,000

The machine shop owner is considering hiring a consultant to ascertain whether the shop will get the government contract. By talking to other shop owners who have hired the consultant, the owner has estimated a 0.7 probability that the consultant would present a favourable report, given that the contract is awarded to the shop, and a 0.8 probability that the consultant would present an unfavourable report, given that the contract is not awarded.

a) The posterior probability of the contract being awarded to the shop, given a favourable report, is equal to:

b) If the consultant presents a favourable report, the optimal decision for the firm is to buy:

c) If the consultant presents an unfavourable report, the optimal decision for the firm would be to buy:

d) The posterior probability of the contract being awarded to the shop, given an unfavourable report, is equal to:

e) The expected value of the firm's optimal decision strategy is equal to:

f) The probability that the consultant will present a favourable report is equal to:

g) The Expected Value of Sample Information is equal to: