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Math Help - conditional probability function

  1. #1
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    conditional probability function

    An urn contains three white, six red, and five black balls. Six of these balls are randomly selected without replacement from the urn. Let X and Y denote the number of white and black balls selected respectively. Compute the conditional probability function of X given that Y = 3. Also compute E[X given that Y = 1].
    I would love some help on this problem.
    I know if Y = 3, the probability that no white balls are selected is (8/11)(7/10)(6/9). I'm not really sure what to do after this. Thanks for your help.
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    P(Y=3)=\frac{{5 \choose 3}{9 \choose 3}}{{14 \choose 6}}

    P(X=1 \text{ and }Y=3)=\frac{{5 \choose 3}{3 \choose 1}{6 \choose 2}}{{14 \choose 6}}
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