MATH: statistic/ probalitity -Randint - need help problem with #3 (a-d) - relate

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MATH: statistic/ probalitity
-Randint
- need help problem with #3 (a-d)
- related questions
- please explain/show steps/answer to the question

In the World Series of baseball, the first team to win four games wins the championship. The series might last four, five, six, or seven games. A fan who buys tickets would like to know how many games, on average, he can expect a championship series to last. Assume the two teams are equally matched, and set aside such potentially confounding factors as the advantage of playing at home. (If you've already completed some intermediate probability, you recognize this as the expected value for the number of games.) 3. a. Simulate a World Series by entering MATH PRB randint(1,2,7) on your calculator. Let a "1" represent Team 1 winning a game, and "2" represent Team 2 winning. You will simulate seven four games See below for an example. the World Series is over and you will ignore any additional games. randInt 1,2,7) 1 1 2 1 1 1 2 b. Record how many games it took to first two games won by Tean 1 win the series. In the example above, it took 5 games. third game won by Team 2 Team 1 wins Serie c. Repeat the simulation at least 25 times. ignore Each time, record the number of games it took to win the World Series. You do not care which team won, you only care how long the series took. Based on your simulation, what is the average number of games played for a World Series? d.

Explanation / Answer

a) The problem here states that two teams are playing a series of games. The team which wins 4 games overall (not necessarily consecutively) before the other team, wins the World Series. Thus atleast 4 games have to be played, otherwise there would be no scope for any team to win 4 games. Also the number of games played between the two teams is at most 7, since one team would obviously have won 4 games by that time. So it is said to generate a series of random numbers consisting of 1's and 2's, where "1" signifies that team 1 has won and "2" signifies that team 2 has won. It has been said to simulate a series of length 7, unless a team has already won 4 times.

b) Performing the simulation for the 1st time, I obtain the following random series

Thus it took 6 games to win the series, since "1" is repeated for the 4th time in the 6th game i.e - Team 1 won for the 4th time in the 6th game. We keep a record of the number 6 here.

c) Next we repeat this simulation process 25 times and each time we keep a record of the number of games needed to proclaim a team as the winner. I am providing the number of games required to proclaim the winner in these 25 simulations (it is not necessary to record which team won)

d) Based on my simulation, the average number of games played for a world series

= (Sum of the number of games required in the 25 simulations) / 25

= (6+5+4+5+7+7+6+6+5+4+7+4+5+4+4+5+5+5+7+4+7+7+6+5+7 ) / 25 =5.48

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