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 18-16 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?

Question

Details and Assumptions:
Clarification: Team A currently has 18 points, expressed via "18-16 for team A".

Answer 1

99/128