Volleyball Probability

Two equally matched teams are playing a game of volleyball. Each team has a \(\frac{1}{2}\) 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 \(\frac{a}{b}\) 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 "18-16 for team A".

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