# Math Help - conditional probability function

1. ## 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.

2. $P(Y=3)=\frac{{5 \choose 3}{9 \choose 3}}{{14 \choose 6}}$

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