Question

A volleyball team is entered in a tournament. Rounds of the tournament are played as best of three; that is, each team will play the opponent in that round until one of the teams has won two games.

Suppose that teams are matched up evenly in the first round of the tournament, such that either team has an equal chance to win. For subsequent games, if a team had just won they will be more confident and more likely to win, whereas if they had just lost they will be demoralized and less likely to win. In rounds two and three, if a team had won the previous game they will win with probability 3/4. Sensibly, if a team had lost the previous game they will win with probability 1/4.

1.)If a team wins the first game of the 3-game round, what is the probability that they win the round overall? Answer

2.)what is the probability that a team loses the round overall if they lose the first game?

Answer 1