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Math Help - find the probability

  1. #1
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    find the probability

    Hello. I am having problems with this prob question, thanks for your help:

    G= guilty
    P(G)= 2/3
    I= innocent
    P(I)= 1/3
    The judge comes to know the result x of the test of DNA of the accused person. If guilty, the probability of x is 90%. If innocent is 5%.

    Which condition on the probability of x, subject to the two events G and I has to be satisfied so that the final probability atributed by the judge to the innocence I is 100%.

    the book says P(x|G)=0. Why? I can't get it. Thank you very much.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by 0123 View Post
    Hello. I am having problems with this prob question, thanks for your help:

    G= guilty
    P(G)= 2/3
    I= innocent
    P(I)= 1/3
    The judge comes to know the result x of the test of DNA of the accused person. If guilty, the probability of x is 90%. If innocent is 5%.

    Which condition on the probability of x, subject to the two events G and I has to be satisfied so that the final probability atributed by the judge to the innocence I is 100%.

    the book says P(x|G)=0. Why? I can't get it. Thank you very much.
    Problem 1 is that you are already told that P(x|G)=0.9


    Ignore that, P(I|x)+P(G|x)=1, so P(I|x)=1 implies P(G|x)=0, so

    P(G|x) = P(x|G)P(G)/P(x)

    P(x)=P(I)P(x|I) + P(G)P(x|G)

    Now assume P(x) != 0, and that P(G) != 0, then P(G|x)=0 implies that
    P(x|G)=0

    RonL
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