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Math Help - Probability!

  1. #1
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    Smile Probability!

    Hi!

    Here's the question I need help with:

    Consider a hypothetical town with population 10,000 in which a man is suspected of a crime. His blood matches a stain found at the scene some time after the crime was committed. 1% of the population will have matching blood. Because in this case the stain is somewhat degraded, the probability of getting a match even if the blood is identical is 0.95

    a) Draw a tree of the different possibilities of the man being guilty or not, and his blood matching or not.
    b) Find the probability of a match.
    c) Find the probability that this man is guilty of the crime and his blood matches.
    d) If there is a match, find the probability that the man is guilty (use Bayes' rule)

    Thanks in advance.
    Last edited by brumby_3; August 27th 2008 at 06:42 PM.
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  2. #2
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    There are four possibilities to consider. They are:

    He is guilty and his blood matches.
    He is guilty and his blood doesn't match.
    He is not guilty and his blood matches.
    He is not guilty and his blood doesn't match.
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  3. #3
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    :)

    What are the percentages for each possibility? This is where I'm getting confused.
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  4. #4
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    Quote Originally Posted by brumby_3 View Post
    What are the percentages for each possibility? This is where I'm getting confused.
    Do you understand conditional probability?

    Pr(not guilty | blood matches) = 0.01.

    etc.
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