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    Posterior probability

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    Using the following information about the accuracy of a market research firm:

    Probability of a favorable study given a favorable market = 0.7
    Probability of an unfavorable study given a favorable market = 0.3
    Probability of a favorable study given an unfavorable market = 0.05
    Probability of an unfavorable study given an unfavorable market = 0.95

    If there is a 0.60 prior probability of a favorable market, find the following possibilities:

    a. the probability of a favorable market given a favorable study.

    b. the probability of an unfavorable market given an unfavorable study.

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    Solution Preview

    Using the following information about the accuracy of a market research firm:

    Probability of a favorable study given a favorable market = 0.7
    Probability of an unfavorable study given a favorable market = 0.3
    Probability of a favorable study given an unfavorable market = 0.05
    Probability of an unfavorable study given an unfavorable market = 0.95

    If there is a 0.60 prior probability of a favorable market, find the following possibilities:

    Prior probability of a favorable market= 0.6 (given)
    Therefore prior probability of an unfavorable market= 0.4 = 1 - 0.6
    ( As probability of favorable market + probability of unfavorable market = 1)
    This is because there are only two possibilities - favorable and unfavorable market and one of them must exist

    Probability of ( A & B happening together) = Probability of A x Probability of B given A

    a. the probability of a favorable ...

    Solution Summary

    The solution calculates posterior probability

    $2.19

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