Two baseball teams (Team A and Team B) are playing a best-of-five games championship series, which means that the first team to achieve three winning games is the winner of the championship. Based on previous experience, Team A has a 42% chance of winning the first game of a series against Team B (and therefore a 58% of losing). During this series, any team that wins a game increases its chances of winning the next game, and any team that loses a game decreases its chances of winning the next game. The table below shows specific changes in probabilities that may occur based on past experience. For example, Team A has a 47% chance of winning against Team B following one previous winning game.
In the sortable table below, click on the column title to organize the table by that column's values.
|Outcome for Team A||Probability of Winning Subsequent Game||Probability of Losing Subsequent Game|
|playing first game of a series against Team B||0.42||0.58|
|after having won one game||0.47||0.53|
|after having won two games in a row||0.55||0.45|
|after having lost one game||0.39||0.61|
|after having lost two games in a row||0.32||0.68|
Decide whether the following statements are true or false about this scenario.
Winning helps Team A’s chances of winning subsequent games by a greater amount than losing hurts Team A’s chances of winning subsequent games.
Team A has a less than 10% chance of sweeping the series by winning three straight games.
Team A’s chance of winning the championship is greater than 35%.