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 $p + q$.


Let's think step by step and output the final answer within \boxed{}.
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