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Math Help - Probability problem, please help!

  1. #1
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    Probability problem, please help!

    Hi, can someone please help me out with this problem? Like step by step on how to solve this?
    Thanks you!

    A company that produces a particular machine component has 3 factories, one each in Buffalo, Detroit, and Pittsburgh. 39% of the components produced come from the Buffalo factory, 36% of the components come from the Detroit factory, and 25% of the components come from the Pittsburgh factory. It is known that 1.1% of the components from the Buffalo factory, 1.4% of the components from the Detroit factory, and 0.9% of the components from the Pittsburgh factory are defective. Given that a component is selected at random and is found to be defective, what is the probability that the component was made in Detroit?
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  2. #2
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    Re: Probability problem, please help!

    Use Bayes' theorem.

    Let X be whether or not there's an error and Y_i which factory the component was made in ( Y_1 is Detroit).

    P(Y_1|X)=\frac{P(X|Y_1)P(Y_1)}{P(X|Y_1)P(Y_1) + P(X|Y_2)P(Y_2)+P(X|Y_3)P(Y_3)}
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  3. #3
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    Re: Probability problem, please help!

    ok so i broke it down and got:

    (0.39)(0.011) = .00429
    (0.36)(0.014) = .00504
    (0.25)(0.009) = .00225


    next i did .00504/[.00504+.00225+.00429]
    =.00504/.01158
    =.43532

    Is this right, or am I doing this completely wrong?
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