There are $4$ boxes with $6$ white balls and $5$ black balls in each. You randomly select a ball from the first box. If the ball is white, the experiment is over. If it is black, you select a ball from the next box. The experiment is over if a white ball is drawn or if you draw a ball from all the boxes. Let $X$ be the number of boxes from which a ball was drawn. Let $Y$ be the number of white balls drawn.
Find the joint probability mass function?
I'm not asking for someone the solve the problem for me, I just need help how to start.
X 1 2 3 4 Y 0 1
How should I determine let's say, $P(X=1, Y=0)$? $P(X=1, Y=0) = P(X=1) * P(Y=0 | X=1) = 6/11 *$ ?