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. 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.

Qn 1.Which of the following describes how a six-sided die could be used to simulate one repetition of a best-of-three series between teams A and B?

1)

Let rolls 1, 2, and 3 represent team A winning a game and 4, 5, and 6 represent team B winning a game. Roll the die and record who wins the game until one team has won two games (two or three times).
2)

Let rolls 1 and 2 represent team B winning a game and 3-6 represent team A. Roll the die and record who wins the game until one team has won two games (two or three times).
3)

Let rolls 1 and 2 represent team A winning a game and 3-6 represent team B. Roll the die and record who wins the game until one team has won two games (two or three times).
4)

There is not a preferred method of the three listed.
Qn 2. Of the methods listed below, select which would be the best use of a six-sided die to approximate the probability that team A would win the best-of-three series against team B.

1)

Let rolls 1, 2, and 3 represent team A winning a game and 4, 5, and 6 represent team B winning a game. Roll the die and record who wins the game until one team has won two games (two or three times). Repeat the simulation 50 times and record how often team A wins divided by the number of repetitions.
2)

There is not a preferred method of the three listed.
3)

Let rolls 1 and 2 represent team A winning a game and 3-6 represent team B. Roll the die and record who wins the game until one team has won two games (two or three times). Repeat the simulation for 100 times and record how often team A wins divided by the number of repetitions.
4)

Let rolls 1 and 2 represent team B winning a game and 3-6 represent team A. Roll the die and record who wins the game until one team has won two games (two or three times). Repeat the simulation a large number of times (say 1000) and record how often team A wins divided by the number of repetitions.
Qn 3.

It turns out that the probability is 0.741 that team A would win this best-of-three series against team B. What does this probability mean? Select all that apply.

1) If teams A and B play a best-of-three series for 1000 times, then team A will win 741 of those series.
2)

None of these statements are correct.
3)

Team A has a higher chance of winning the best of three series than the 2/3 chance of winning any one game).
4)

All of these statements are correct.
5)

If teams A and B repeatedly play a best-of-three series, then in the long run team A will win 74.1% of those