Oscar Weng is planning to raise funds to pay for a scouting trip by running a concession stand during tomorrow’s high school soccer game. Oscar needs to decide whether to rent a large insulated thermos from the local rental store and sell cocoa at the game or to rent a large refrigerated container and sell lemonade.
Unfortunately, Oscar does not have the resources to rent both items. Sales depend on whether it is sunny or rainy during the game. If the weather is sunny, Oscar will make a profit of $60 from lemonade but only $20 from cocoa. If, however, it is rainy, Oscar will make a profit of $80 from cocoa but only break even if he brings lemonade. Based on the local newspaper’s prediction, Oscar thinks there is a 60% chance of it being sunny tomorrow.
Oscar’s older brother Elmo, who has earned the Meteorology Badge, claims he can predict the weather more accurately than the newspaper. For only $4, he offers to study the weather and tell Oscar if there is a “good chance” or “bad chance” of it being sunny tomorrow. Assume that the following data are avail-able about the accuracy of the brother’s information:
• The probability that he will say “good chance” is 0.7.
• If he says “good chance,” then there is a 0.83 probability that it will actually be sunny tomorrow.
• If he says “bad chance,” then there is only a 0.25 probability that it will actually be sunny tomorrow.
(a) Draw the complete decision tree for Oscar’s problem and fold it back to help him decide what he should do.
(b) How much is his brother’s information actually worth to Oscar?