Problem: In an urn there are A yellow, B green and C blue ball. In each round we extract one ball and then place it back into the urn. We extract the balls until we extract a blue one, after we have already extracted at least one yellow and one green ball. What is the distribution of random variables X(number of blue balls that have been extracted) and Y(number of all extractions)?
I was thinking to start with a problem until we extract balls of all colors and then divide it into a problem where the last ball is blue and where the last ball isn't blue. I don't know how to go about it. Should I go for a different approach?