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 | 0.4 | 0.55 | 0.42 | 0.56 | 0.55 | 0.39 | 0.52 |
Solution :
From given data,
Game (X) | 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) What is the probability that the Atlanta Braves win the World Series? If required, round your answer to two decimal places.
P (That the Atlanta Braves win the World Series) = P(X = 2)
= 0.55
The probability that the Atlanta Braves win the World Series is 0.55
B.) What is the average number of games played regardless of winner? If required, round your answer to one decimal place.
E (X) = x p(x)
= (1* 0.4) + (2* 0.55) + (3* 0.42) + (4* 0.56) + (5* 0.55) + (6* 0.39) + (7* 0.52)
= 0.4+1.1+1.26+2.24+ 2.75+2.34+3.64
= 13.73
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