# Aberystwyth University the Payoff from The Best Outcome

1.

a. Let the payoff from the best outcome, the value in cell A3, vary from \$30,000 to \$50,000 in increments of \$2500.

When the payoff from the best outcome is equal to \$45,000, Decisions 1 and 3 are tied for best. Decision 3 is the best for lower payoffs, whereas Decision 1 is the best for higher payoffs.

b. Let the probability of the worst outcome for the first decision, the value in cell B5, vary from 0.7 to 0.9 in increments of 0.025, and use formulas in cells B3 and B4 to ensure that they remain in the ratio 1 to 2 and the three probabilities for decision 1 continue to sum to 1.

Decision 3 is the best for every value of the probability of the worst outcome, with the exception of a probability of 0.70 where Decision 1 is the best.

c. Use a two-way data table to let the inputs in parts (a) and (b) vary simultaneously over the indicated ranges.

Decision 3 is always the best, with the exception with probability of the worst outcome equal to 0.

Questions 2-6 (15 points)

2. The mean of the probability distribution is also called the: expected value (d)

3. Expected monetary value (EMV) is: the weighted average of possible monetary values, weighted by their probabilities (c).

4. In decision trees, EMVs are calculated through a “folding back” process (d).

5. In a single-stage decision tree problem, you make decisions first and then all you wait to see an uncertainty outcome (a).

6. Expected monetary value is the weighted sum of the possible monetary outcomes [True]