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# Decision Tree and Probability

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Problem:
Bill Holiday is not sure what he should do. He can either build a quadplex (i.e., a building with four apartments), build a duplex, gather additional information, or simply do nothing. If he gathers additional information, the results could be either favorable or unfavorable, but it would cost him \$3,000 to gather the information. Bill believes that there is a 50-50 chance that the information will be favorable. If the rental market is favorable, Bill will earn \$15,000 with the quadplex or \$5,000 with the duplex. Bill doesn't have the financial resources to do both. With an unfavorable rental market, however, Bill could lose \$20,000 with the quadplex or \$10,000 with the duplex. Without gathering additional information, Bill estimates that the probability of a favorable rental market is 0.7. A favorable report from the study would increase the probability of a favorable rental market to 0.9. Furthermore, an unfavorable report from the additional information would decrease the probability of a favorable rental market to 0.4. Of course, Bill could forget all of these numbers and do nothing. What is your advice to Bill?