Chapter 9, Problem 4P

Long or Short World Series? In the World Series the top teams in the National League and the American League play a best-of-seven series: that is, they pay until one team has won four games. (No tie is allowed, so this results in a maximum of seven games.) Suppose the teams arc evenly matched, so the probability that either team wins a given game is $\frac{1}{2}$ .

(a) Use a coin or a modeling program to model a World Series. in which ‘heads” represents a win by Team A and “tails” represents a win by Team B. Perform this experiment go times, keeping track of how many games are needed to decide each series. Estimate the probability that an evenly matched series will end ¡n four games.
Do the same for five, six, and seven games.

(b) What is the probability that the series will end in four games? Five games? Six games?
Seven games? Compare with your estimates from part (a).

(c) Find the expected value for the number of games until the series ends. [Hint: This will be $P(fou{r}^{}games)\times 4+P(five)\times 5+P(six)\times 6+P(seven)\times 7$ .]