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Math Help - Conditional Probability

  1. #1
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    Conditional Probability

    Hey

    I've just been stuck on this question for a while and can't seem to figure out how to do it. I would appreciate any help.

    Problem:

    Consider 3 urns. Urn A contains 2 white and 4 red balls, Urn B contains 8 white and 4 red balls, and Urn C contains 1 white and 3 red balls. If 1 ball is selected from each urn, what is the probability that the ball chosen from urn A was white given that exactly 2 white balls were selected.

    Thanks!
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  2. #2
    MHF Contributor matheagle's Avatar
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    You need to compute P(A|B)={P(AB)\over P(B)}

    Where
    A=ball chosen from urn A was white
    and
    B=exactly 2 white balls were selected.
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  3. #3
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    Sorry, but I don't know how to format my symbols to get them to look like yours but,

    I did do that and I got

    P(AlB) = P(BlA)(PlA)/(P(BlA)P(A) + P(BlAc)P(Ac))

    Where Ac is complement of A.

    And I dont really know what to put for P(BlA) and P(BlAc)
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  4. #4
    MHF Contributor matheagle's Avatar
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    I don't know about all that A-complement stuff
    JUST write down what B and AB are....
    and figure out the probability of those events

    FOR example, the event AB isn't so hard.
    It consists of two mutually exclusive events... W_1R_2W_3 OR W_1W_2R_3

    where the subscript denotes which urn.
    BY independence and since we are only selecting ONE marble, that probability is

    (2/6)(4/12)(1/4)+(2/6)(8/12)(3/4)

    B consists of those two events and only one more ... R_1W_2W_3
    Last edited by matheagle; October 13th 2009 at 08:22 PM.
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  5. #5
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    Answer for your question

    -
    Last edited by Math Quest; October 13th 2009 at 06:15 PM.
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