HOW MANY GAMES IN A WORLD SERIES?

In baseball’s World Series, the first team to win four games wins the championship. The series might last four, five, six, or seven games. A fan who buys tickets would like to know how many games, on average, he can expect a championship series to last. Assume the two teams are equally matched, and set aside such potentially confounding factors as the advantage of playing at home. We want to know the expected value for the number of games that will be played in the World Series. 

1. Simulate a World Series on your calculator or computer. Let a “$1$” represent Team $1$ winning a game, and a “$2$” represent Team $2$ winning. You will simulate seven “games,” but as soon as one team wins four games the World Series is over and you have to ignore any results that follow that. See below for an example.

   Record how many games it took to win the series. In the example at right, it took $5$ games.

   Repeat the simulation at least $25$ times. Each time, record the number of games it took to win the World Series. You do not care which team won, you only care how long the series took.

2. Based on your simulation, what is the average number of games a World Series lasts?

   Hint (b):

   Theoretically, the series is expected to last for $5.8125$ games.
   Was your simulation close?