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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