Tristan is eating his favorite cereal, Tiger Crunch, which has marshmallows of two colors, black and orange. He eats the marshmallows by randomly choosing from those remaining one at a time, and he starts out with 17 orange and 5 black marshmallows. If \frac{p}{q} is the expected number of marshmallows remaining the instant that there is only one color left, and p and q are relatively prime positive integers, find p+q.