# combinatorics – Combinatorical problem with additional layer of probabilities

Suppose you have a bag with $$R$$ red balls, $$G$$ green balls, and $$Y$$ yellow balls.
Each red balls has probability $$p$$ to vanish when you draw it. Each green and yellow ball has probability $$q$$ to vanish when you draw it. (If a ball vanishes it does not come back into the bag.)

What is the probability that the first non-vanishing ball that you draw out of the bag is green?