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    Decision Trees

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    Please give name of program used to solve problem and details on how you solved each problem.

    3-21 During the next year, Allen must decide whether to invest $10,000 in the stock market or in a CD at an interest rate of 9%. If the market is is good, Allen believes that he could get a 14% return on his money. With a fair market, he expects to get an 8% return. If the market is bad, he will most likely get a 0% return. Allen estimates that the probability of a good market is 0.4, the probability of a fair market is 0.4, and the probability of a bad market is 0.2, and he wishes to maximize his long-run average return.

    a. Develop a decision table for this problem
    b. What is the best decision?

    3-28. A group of medical professionals is considering the contruction of a private clinic. If the medical demand is high (there is a favorable market for the clinic) the physicians could realize a net profit of $100,000. If the market is not favorable, they could lose $40,000. If they don't proceed at all there is $0 cost. In the absence of any market data, the best the physicians can guess is that there is a 50-50 chance the clinic will be successful.

    Construct a decision tree to help analyze this problem.
    What should the medical professional do?

    3-29. The physicians from problem 3-28 above have been approached by a market research firm that offers to perform a study of the market at a fee of $5,000. They say the Byes' theorem allows them to make the following statements of probability:

    probability of a favorable market given
    a favorable study=0.82
    probability of an unfavorable market given
    a favorable study=0.18
    probability of a favorable market given
    an unfavorable study=0.11
    probability of a unfavorable market given
    an unfavorable study=0.89
    probability of a favorable research
    study=0.55
    probability of an unfavorable research
    study=0.45

    a) Develop a new decision tree for the medical professionals to reflect the options now open with the market study.
    b) Use the EMV approach to recommend a strategy.
    c) What is the expected value of sample information? How much might the physicians be willing to pay for a market study?

    © BrainMass Inc. brainmass.com October 9, 2019, 6:58 pm ad1c9bdddf
    https://brainmass.com/statistics/probability/decision-trees-103724

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    Solution Preview

    See the attached files for the decision trees. I didn't use a program to solve these problems, just the calculations you'll see below.

    Ch.3pg.104

    3-21 During the next year, Allen must decide whether to invest $10,000 in the stock market or in a CD at an interest rate of 9%. If the market is is good, Allen believes that he could get a 14% return on his money. With a fair market, he expects to get an 8% return. If the market is bad, he will most likely get a 0% return. Allen estimates that the probability of a good market is 0.4, the probability of a fair market is 0.4, and the probability of a bad market is 0.2, and he wishes to maximize his long-run average return.

    a. Develop a decision table for this problem

    b. What is the best decision?

    Invest in Stock Market Invest in CD

    Good market Fair Market Bad Market
    (0.4) (0.4) (0.2)

    14% return 8% return 0% return 9% return

    Allen can either decide to invest in the stock market or invest in a CD. Because the CD has a fixed rate, it doesn't matter what the market is like ... he'll always get a 9% return. The stock market can give him ...

    $2.19