How Many Games Does it Take to Win the World Series?

In order to determine the champion of Major League Baseball in the U.S. and Canada, the winners from the National League and the American League play the "World Series." The Series consists of seven games. If a team wins four out of the seven games, they are the champions.

Of course, all seven games are not played if a team has already won four. Thus, what we want you to find out is how many games do you expect to be played before a team wins four games and becomes the champion?

Predicting how long a series will take is not easy. There are many factors that are involved: Where are they playing? Is anyone injured? What is the weather like?

For the purpose of this problem, however, we will simplify these into one question... What is the probability that the National League (NL) will win an individual game?

You are welcome to make that probability whatever you like (depending upon whether or not you prefer NL teams or AL teams), but we suggest that you begin by making the chances 50-50 (probability = 1/2 = .5) and then play with different probabilities later.

Questions:

1. What is the least number of games that could be played and still have a champion?

2. What is the greatest number of games that would be played?

3. What sort of model could you use for this problem?

4. How would you solve this problem analytically?

5. How would changing the probability of the NL winning an individual game affect your model?