# Math

The Houston Rockets and San Antonio Spurs will play a "best two out of three" series. Assume that Houston has a probability of 1/3 of winning any game.

a. Draw a probability tree showing possible outcomes of the series. Label the branches with appropriate probabilities.

b. What is the probability that Houston wins in two straight games? that San Antonio wins in two straight games?

c. what is the probability that the series goes to three games?

d. what is the probability that Houston wins the series after losing the first game?

e. What is the probability that San Antonio wins the series?

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1. prob(H win) = 1/3 , prob(A win) = 2/3
prob(H loss) = 2/3 , prob(A loss) = 1/3

a) not good on trees in this forum, hard to show

b) Prob (HH) = (1/3)(1/3) = 1/9
Prob(AA) = (2/3)(2/3) = 4/9

c) to go 3 games, could be
AHA or HAH
prob of that = (2/3)(1/3)(2/3) + (1/3)(2/3)(1/3) = 4/27+2/27
= 6/27
= 2/9

d) has to be AHH , showing the winning results
prob(AHH) = (2/3)(1/3)(1/3) = 2/27

e) three ways for Antonio to win the series
1. AA -----> (2/3)(2/3) = 4/9
2. AHA ---->(2/3)(1/3)(2/3) = 4/27
3. HAA ----> (1/2)(2/3)(2/3) = 4/27

prob(A wins series) = 4/9 + 2(4/27) = 20/27

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