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?