Question

1.

The following is a payoff table giving profits for various situations.

Alternatives	A	B	C
Alternative 1	120	140	120
Alternative 2	200	100	50
Alternative 3	100	120	180
Do Nothing	0	0	0

A recent forecast showed a 40% likelihood of A, a 10% likelihood of B, and a 50% likelihood of C. The decision criterion that now should be used to solve this problems is known as

a. Equal Likelihood

b. Expected Opportunity Loss

c. Maximax

d. Expected Value

e. Unclear

2.

The following is a payoff table giving profits for various situations.

Alternatives	A	B	C
Alternative 1	120	140	120
Alternative 2	200	100	50
Alternative 3	100	120	180
Do Nothing	0	0	0

A recent forecast showed a 40% likelihood of A, a 10% likelihood of B, and a 50% likelihood of C. This problem has how many states of nature?

a. 4

b. 3

c. 1

d. 2

Answer 1

(1) Option (d)

(a) Equal likelihood: This is the criterion when the probability of each state of nature is same. For instance, the likelihood of A, B, and C is 1/3,1/3,1/3. Here, the likelihood is 40%,10%, and 50% respectively. Hence, option (a) is incorrect.

(b) Expected opportunity loss is the criterion where the payoff of each event is deducted from the highest payoff and the regret is calculated. Hence, option (b) is incorrect.

(c) Maximax is the criterion where the best of the best payoff is selected. Hence, option (c) is incorrect.

(d) Expected value is the criterion, where the value is calculated based on the probability of occurrence of each element in the decision table. Hence, option (d) is correct.

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(2)

The state of the nature refers to the possible outcomes that can happen in the future.

In this question three possible outcomes for each alternative are there. Hence, states of nature are 3.

Correct answer: option (b)

Hope the answer will help. Thank you.