Teams A and B are playing a series of games. The series is over as soon as a team wins a total of three games. Team A is two times more likely to win a game than Team B. What is the probability that Team A wins the series?
The probability that A will win is 2/3 and that B will win is 1/3 so if A wins three times in a row, 2/3*2/3*2/3=8/27.