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14 April, 01:49

Suppose that the four inspectors at a film factory are supposed to stamp the expiration date on each package of film at the end of the assembly line. john, who stamps 20% of the packages, fails to stamp the expiration date once in every 200 packages; tom, who stamps 60% of the packages, fails to stamp the expiration date once in every 100 packages; jeff, who stamps 15% of the packages, fails to stamp the expiration date once in every 90 packages; and pat, who stamps 5% of the packages, fails to stamp the expiration date once in every 200 packages. if a customer complains that her package of film does not show the expiration date, what is the probability that it was inspected by john?

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  1. 14 April, 01:51
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    Think through the following events:

    A: the produce is not marked

    B1: the produce is marked by John

    B2: the produce is marked by Tom

    B3: the produce is marked y Jeff

    B4: the produce is marked by Pat

    Applying the rule of elimination, the formula would be:

    P (A) = P (B1) P (A|B1) + P (B2) P (A|B2) + P (B3) P (A|B3) + P (B4) P (A|B4)

    And the following are the probabilities:

    P (B1) P (A|B1) = (.20) (1/200) =.001

    P (B2) P (A|B2) = (.60) (1/100) =.006

    P (B3) P (A|B3) = (.15) (1/90) =.00167

    P (B4) P (A|B4) = (.05) (1/200) =.00025

    The likelihood that the product is not imprinted is equal to. 001 +.006 +.00167 +.00025 =.00892

    The probability that it was reviewed by John is =.001/.00892 =.1121
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