In Urn No. 1 (first urn) there are $y$ balls, of which $x$ white balls and $y-x$ black balls. In Urn No. 2 (second first) there are $y$ balls again, but the white balls are $y-x$. You randomly take a ball from the first urn and place it in the second urn. Then, from the second urn you randomly take a ball and place it in the first urn.
Calculate the probability distribution of $A_r$ = "in the first urn there are at the end $r$ white balls".
Do you have any advice? I was thinking of applying the binomial distribution, but I would not be sure to proceed.
I thank anyone who can help me.