Problem: I have 12 balls in a bag consisting of 9 blue and 3 red. I randomly choose 5, (each combination is equally likely). Now I check to see among the 5 removed balls, if they are exactly 2 RED balls. Stop here if so. If not, put the 5 balls back into bag and shake. Keep repeating this process until you get 2 red balls.
I want to calculate the expected number of times you need to removed the 5 balls from this bag, until you get your desired result.
I am struggling to understand, what distribution this could be? It's obviously not binomial, but I don't see what else it could be.
Please help - :)