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Math Help - Probability.

  1. #1
    Len
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    Probability.

    Company A produces 60%of the total output and Company B produces the rest(40%). 5% of the goods for Company A and 10% for company B are defects.

    If a good is randomly selected what is the chance of it being a defect.

    I have P(Defect)= P(Defect A) + P(Defect B)
    =0.6*0.05+0.4*.1=0.07

    If a good is known to be a defect what is the probability it was produced by Company A.

    This one I am stuck on, any help would be appreciated
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  2. #2
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    Let D = defect.

    You want:
    P(A|D)
    = P(A union D)/P(D)
    = (0.6*0.05)/0.07
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  3. #3
    Flow Master
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    Quote Originally Posted by actsci231 View Post
    Let D = defect.

    You want:
    P(A|D)
    = P(A {\color{red}\cap} D)/P(D)
    = (0.6*0.05)/0.07
    Small correction in red. The numerical calculation is not affected.

    I will also point out that this question is easily done by first drawing a tree diagram. Made by Company A and Made by Company B are the first two branches. Defective and not defective are the next two branches.
    Last edited by mr fantastic; November 3rd 2008 at 03:45 AM. Reason: Added the second sentence.
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  4. #4
    Len
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    Alright that makes sense, the probability of Company A defect/ divided by the probability of a defect. Thanks a lot.
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