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    Managerial Statistics - Conditional Probability Question

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    Management of a golf ball company has carefully screened and selected 12 dozen golf balls, and it is agreed that this sample contains 15 nonconforming balls (all for various cosmetic reasons). The balls are given to an inspector for classification into "good" and "bad" piles. The inspector ends up rejecting 7 good balls, and accepting 6 bad balls. The inspector classifies the remaining balls in the sample correctly.

    a. On average, what is the probability that this inspector will reject a golf ball? Enter your response rounded to three decimal places.

    b. On average, what is the probability that this inspector will make a wrong decision? Enter your response rounded to three decimal places.

    c. On average, what is the proportion of accepted units that are actually nonconforming? Enter your response rounded to three decimal places.

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    Solution Preview

    Total Golf Balls = 12*12 = 144
    Bad Balls = 15
    Good Balls = 144 - 15 = 129

    a.
    Balls Inspector Rejected: 7 good balls + [15-6 (accepted)] ...

    Solution Summary

    A question on conditional probability

    $2.19