Previous Exercise:P.3.5*Suppose that baseball Team A is better than baseball Team B. Team A is enough better that it has a 2/3 probability of beating Team B in any one game, and this probability remains the same for each game, regardless of the outcomes of previous games.

1. Explain what it means to say that Team A has a 2/3 probability of beating Team B in any one game.
2. If Team A plays Team B for 3 games, is Team A guaranteed to win exactly twice?
3. If Team A plays Team B for 30 games, is Team A guaranteed to win exactly 20 times?
4. If Team A plays Team B for 30 games, do you think it's very likely that Team A will win exactly 20 times? Explain.

1. If these two teams play each other many, many times under identical conditions, Team A will win 2/3 of the games in the long run.
2. No, this is a long-run proportion, not the proportion for every set of 3 games.
3. No, although we expect the proportion to tend to be closer to 2/3, this is still not a guarantee.
4. We expect the proportion of games that Team A wins to be close to 2/3, but with so many different possibilities that are also close to two-thirds (such as 18, 19, 21, 22 wins), there could still be a low probability that A wins exactly 2/3 of the 30 games.

P.3.6Reconsider the previous exercise. Continue to assume that Team A has a 2/3 probability of beating Team B in any one game. Now suppose that Team A and Team B play a best-of-three series, meaning that the first team to win two games wins the series.

1. If you are a fan of Team A, would you prefer to play a single game or a best-of-three series or would you have no preference? Explain.
2. Describe how you could use a six-sided die to simulate one repetition of a best-of-three series between Teams A and B.
3. Describe how you could use a six-sided die to approximate the probability that Team A would win the best-of-three series against Team B.
4. It turns out that the probability is 0.741 that Team A would win this best-of-three series against Team B. Interpret what this probability means.