Conditional Probability and Conditional Expectation Question
Here's the question
An urn contains three white, six red, and five black balls. Six of these balls are randomly selected from the urn. Let X and Y denote respectively the number of white and black balls selected. Compute the conditional probability mass function of X given that Y=3. Also compute E[X|Y=1].
I have it worked out and attached as a .pdf. I was hoping that someone would be able to check out the work and make sure that I'm on the right track, or point out what I'm doing wrong. Thanks