4 a In the baseball playoffs teams play a series of games to

4. a) In the baseball playoffs teams play a series of games to decide the winner in each round. The first round is a 5 game series. If the teams split first two games it suggests that they are evenly matched so that the probability of each team winning any of the next three games is 1/2 for each game. If team A wins game three, what is the probability that Team A will win the series?

b) In the 2004 American League Championship Series, New York won the first 3 games of the 7 game series against Boston. These teams had played nearly 70 games over the previous three years and had evenly split those games. Assuming this result reflects that the probability of either team winning is 50% calculate the probability that Boston would win the next four games and, therefore, the series, if the outcome were purely statistical.

Solution

a) Probability of A winning the series = 1 - Probability of A losing the series

Now, A losses the series if and only if B wins both the 4^th and 5^th match.

P(B wins match 4) = 1/2 = P(B wins match 5)

Now, P(B wins both match 4 and 5) = 1/2 x 1/2 = 1/4

Thus, Probability of A losing the series = 1/4

Therefore, Probability of A winning the series = 1 - Probability of A losing the series = 3/4

b) Probability of Boston wining a game = 1/2

Probability that Boston wins the series, i.e., all the remaining 4 games = 1/2 x 1/2 x 1/2 x 1/2 = 1/16