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 and the Minnesota Twins are playing 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 0.60 0.55 0.48 0.45 0.48 0.55 0.50 Conduct a simulation study with 1,000 trial. Using the summary statistics gathered, answer the following questions:

1. What is the probability that the Atlanta Braves win the World Series?

2. What is the average number of games played regardless of winner?

Answer 1

EXCEL FORMULAS:

B7 =RAND()<=B$2 copy to B7:H506

I7 =COUNTIF(B7:H7,TRUE)>=4 copy to I7:I506

J7 =IF(OR(COUNTIF(B7:E7,TRUE)=4,COUNTIF(B7:E7,TRUE)=0),4,IF(OR(COUNTIF(B7:F7,TRUE)=4,COUNTIF(B7:F7,TRUE)=1),5,IF(OR(COUNTIF(B7:G7,TRUE)=4,COUNTIF(B7:G7,TRUE)=2),6,7))) copy to J7:J506

M7 =COUNTIF(I7:I506,TRUE)/COUNT(A7:A506)  

M9 =AVERAGE(J7:J506)

a) Probability that the Atlanta Braves win the World Series = 0.514 ~ 0.51 (rounded-off to 2 decimals)

b)  Average number of games played regardless of winner = 5.824 ~ 5.8 (rounded-off to 1 decimal)