Find the Expected Value of the Optimal Strategy

Multiple Choice

Find the expected value of the optimal strategy.
-A backpacker is planning a three-day trip in the backcountry with a friend. She wishes to keep the weight of her pack to a minimum. She has decided to bring either rock climbing shoes or an extra fleece jacket but not both. The fleece jacket will be useful if the weather is cold. The rock climbing shoes will be useful if the weather is warm. In trying to decide which of these two items to bring, the backpacker decides on the utilities shown in the following payoff matrix:

According to the weather forecaster, the probability of cold weather is 0.4 . The backpacker selects the item that will maximize the expected utility. What is the expected utility in this case?

A) 6.4
B) 7.6
C) 18.4
D) 12.6