Team A and Team B are playing in the world series. The two teams plays 7 games, the first team to win 4 wins the world series. Team A has won 3 games and Team has won 1 game. Each game is independent of another. The probability of team A winning any single game is 0.55. What is the probability that team A would go on to win the world series?
I have searched the web and am having trouble finding a good example that I understand and isn't starting at the beginning of a series.
From creating a decision tree I have gotten the below. Am I on the right track? I am not sure what my next steps are. P(win game 5)=0.55 P(win game 6)=0.45*0.55 = 0.2475 P(win game 7)=0.45*0.45*0.55 = 0.111375 0.55 + 0.2475 + 0.111375 = 0.908875 P(loose) = 0.45*0.45*0.45 = 0.091125