Question 149
Bryce has $7$ blue socks and $7$ red socks mixed in a drawer. He plays a game with Sean. Blindfolded, Bryce takes two socks from the drawer. Sean looks at the socks, and if they have the same color, Sean gives Bryce $1$ point. Bryce keeps drawing socks until the drawer is empty, at which time the game ends. The probability that Bryce's score is at most $2$ can be written in the form $p / q$, where $p$ and $q$ are relatively prime positive integers. Find $p+q$.