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Math Help - probability with multiple factors

  1. #1
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    probability with multiple factors

    Hi, this question is another one that I can't seem to arrive at a correct answer on.
    Suppose that you're thinking about buying a used R-car at Honest Abe's. In order to make an informed decision you look up the records in an auto magazine and find that 30% of these cars have a faulty transmission. To get more information you hire a mechanic who is excellent: Of all the faulty cars he has examined in the past he correctly judged that 90% were "faulty" and only erroneously judged 10% as "OK." He's almost as good at judging good cars: Of all the good cars he's correctly judged that 80% were "good" and only erroneously judged 20% as "faulty."

    What is the probability that the R-car you're thinking of buying has a faulty transmission if the mechanic judges it to be "faulty"?




    a. .72

    b. .80

    c. .16

    d. .66

    e. .30

    I feel like I'm doing the math as is it was described in the lecture but I'm not coming up with answers that are options in the multiple choice.
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  2. #2
    Senior Member MaxJasper's Avatar
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    Re: probability with multiple factors

    (c) 0.165
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  3. #3
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    Re: probability with multiple factors

    Can you explain to me how you got to that solution. I'm trying to actually understand the math so I can do it on my own.
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  4. #4
    Senior Member MaxJasper's Avatar
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    Lightbulb Re: probability with multiple factors

    Probabilities of:

    mf = mechanic says car is faulty
    f = car is faulty


    P(\text{mf})=\frac{.90+.20}{.90+.10+.20+.80}=.55

    P(f)=.30

    Then the conditional prob(car=faulty when mech says faulty):

    P(f|\text{mf})=.55*.30=.165
    Last edited by MaxJasper; September 9th 2012 at 03:32 PM.
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  5. #5
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    Re: probability with multiple factors

    Thanks again, this makes a lot more sense now, I'm pretty sure I had the matrix setup backwards.
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