An urn contains three white, six red, and five black balls. Six balls are random

Question

An urn contains three white, six red, and five black balls. Six balls are randomly selected from the urn. When a ball isselected, its color is noted and it is put back in the urn beforethe next selection. Let X and Y denoterespectively the number of white and black balls selected. Find theconditional probability mass function of X given thatY=3. Also find E[X|Y=1].

I am having problem finding the probability of how many white ballsare in the urn if they tell you that there is 3 black ballsselected. I can figure the rest out after this part.

Explanation / Answer

this is a replacement probability problem. the no. of ballsremain the same at the starting of any selection. there are 3 whiteballs.

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