Question

Baseball's World Series is a maximum of seven games, with the winner being the first team to win four games. Assume that the Atlanta Braves are playing the Minnesota Twins in the World Series and that the first two games are to be played in Atlanta, the next three games at the Twins' ballpark, and the last two games, if necessary, back in Atlanta. Taking into account the projected starting pitchers for each game and the home field advantage, the probabilities of Atlanta winning each game are as follows:

Game	1	2	3	4	5	6	7
Probability of Win	0.4	0.55	0.42	0.56	0.55	0.39	0.52

a. Set up a spreadsheet simulation model in whether Atlanta wins each game is a random variable. What is the probability that the Atlanta Braves win the World Series? If required, round your answer to two decimal places.

b. What is the average number of games played regardless of winner? If required, round your answer to one decimal place.

Answer 1

The following steps are used to simulate the winner of each game

• Generate a random number from uniform distribution in the interval (0,1) using =RAND()
• If the random number of less than the probability of Atlanta winning that particular game, then the winning team is Atlanta, else the winning team is Minnesota Twins
  • for example if the random number generated for game 1 is 0.55, then the winning team is Minnesota Twins as 0.55 is greater than 0.4 (the probability of Atlanta winning game 1)

For games 5,6, and 7 we will stop the series  if 4 games are already won by either of teams

Prepare the following sheet

Columns A to E

Columns F:G

Columns H:J

The rest

Duplicate the rows, such that you have 1000 trials

Paste the rows as values, if you do not want the regeneration of random numbers

Get the following

a) ans: The probability that the Atlanta Braves win the World Series is 0.45

b) the average number of games played regardless of winner is 5.8