Teams A and B play a series of games with the first team to

Teams A and B play a series of games with the first team to win 5 games being declared the winner of the series. Suppose the probability that team A has .3 probability of winning each game. Given that team A win the first game, what is the probability that team A is the winner of the series

Solution

Team A will be a winner if the team can win 5 consecutive games.Suppose the probability that team A has .3 probability of winning each game.

Thus, the required probability is: 0.3^5=0.00243