b If two items are sampled without replacement what is the p

b) If two items are sampled without replacement, what is the probability that both are good? c) If two items are randomly sampled without replacement, what is the probability that the first is good but the second is defective? Problem 4 A plant manager considers the operational cost per hour of five machine alternatives. The cost per hour is sensitive to three potential weather conditions: cold, mild, and warm. The following table represents the operations cost per hour for each alternative-state of nature combination:

Solution

a. An optimistic decision maker will look at the minimum cost for each alternative.

So the alternative with the lowest minimum cost is Machine 4 ($25)

b. A pessimistic decision maker will look at the maximum cost for each alternative.

So the alternative with the lowest maximum cost is Machine 5 ($45)

c. An equally likely decision maker will assume that cold mild and warm are equally likely to occur with probability = 1/3. So expected costs from all the machines:

Machine 1: 1/3*50 + 1/3*40 + 1/3*45 = 45

Machine 2: 1/3*45 + 1/3*42 + 1/3*47 = 44.67

Machine 3: 1/3*40 + 1/3*35 + 1/3*54 = 43

Machine 4: 1/3*60 + 1/3*25 + 1/3*48 = 44.33

Machine 5: 1/3*45 + 1/3*40 + 1/3*45 = 42.67

So machine with the lowest cost = Machine 5.

d. Expected monetary values for all machines:

Machine 1: 0.30*50 + 0.50*40 + 0.20*45 = 44

Machine 2: 0.30*45 + 0.50*42 + 0.20*47 = 43.9

Machine 3: 0.30*40 + 0.50*35 + 0.20*54 = 40.3

Machine 4: 0.30*60 + 0.50*25 + 0.20*48 = 40.1

Machine 5: 0.30*45 + 0.50*40 + 0.20*45 = 42.5

So machine with the lowest expected cost: Machine 4