# Ending the draw

I have a bag containing 20 red balls and 16 blue balls. I uniformly randomly take balls out from the bag without replacement until all balls of a color have been removed. If the probability that the last ball I took was red can be represented as $$\frac{p}{q}$$, where $$p$$ and $$q$$ are coprime positive integers, find $$p+q$$.

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