Probability
posted by hmmm .
Two equally matched teams are playing a game of volleyball. Each team has a 1/2 chance of winning each point. The game ends once one of the teams gets to a score of 21. If the score is currently 1816 for team A, the probability that team A will win the game can be expressed as a/b where a and b are coprime positive integers. What is the value of a+b?
Details and Assumptions:
Clarification: Team A currently has 18 points, expressed via "1816 for team A".

99/128