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Math Help - Probability of Innocence?

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    Probability of Innocence?

    A defendant is being tried for murder and the only evidence against him is that a tissue sample from the scene matches his. The prosecution believe that there is a 1/10,000 chance of making that match by chance.It is known the guilty party lives in a village of 35,000 people. The defendant is also from that village. Use Bayes' Theorum to work out the probability that the defendant is innocent. Highlight any assumptions you make.
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    Quote Originally Posted by hc215 View Post
    A defendant is being tried for murder and the only evidence against him is that a tissue sample from the scene matches his. The prosecution believe that there is a 1/10,000 chance of making that match by chance.It is known the guilty party lives in a village of 35,000 people. The defendant is also from that village. Use Bayes' Theorum to work out the probability that the defendant is innocent. Highlight any assumptions you make.
    What thoughts have you had? What have you tried? Where are you stuck?
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    Pr(Innocent|Village) = Pr(Village|Innocent) Pr(Innocent) / Pr(Village)
    If you take Pr(Village) = 1
    With Pr(Village|Innocent) = 34999/35000
    Pr(Innocent) = 1/10000
    You get Pr(Innocent|Village) = 0.01%

    That's what I've tried, using Bayes, but I'm just a little hazy on whether or not I've got the right Pr(Village|Innocent) and Pr(Village), where I've made the assumption the Population is closed to that of the Village...
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    Quote Originally Posted by hc215 View Post
    Pr(Innocent|Village) = Pr(Village|Innocent) Pr(Innocent) / Pr(Village)
    If you take Pr(Village) = 1
    With Pr(Village|Innocent) = 34999/35000
    Pr(Innocent) = 1/10000
    You get Pr(Innocent|Village) = 0.01%

    That's what I've tried, using Bayes, but I'm just a little hazy on whether or not I've got the right Pr(Village|Innocent) and Pr(Village), where I've made the assumption the Population is closed to that of the Village...
    Read this: Prosecutor's fallacy - Wikipedia, the free encyclopedia and related pages found using Google.
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