World Series Model
- Use a coin and let each side represents a team (heads = NL; tails = AL).
- Flip the coin to see which team wins a given game.
- Continue flipping the coin until an one of the teams wins the series (one side of the coin appears four times).
- Count how many coin flips (games played) it took for someone to win the series.
- Repeat steps 2-4 many times.
- Average the number of games it took to win each series (this is your estimate of the expected value).
There are many other possible ways to model this problem. Can you think of any?
What model would you use if the probability of the NL winning an individual game = 1/3?... or 1/4?... or 1/10?
Sometimes it can be handy to refer back to the original problem for insight.
Your computer can run these trials much more quickly than any human can. If you have a Macintosh, you can download a handy program for solving this problem.
Once you have run some experiments and come up with some expected values, try your hand at finding an analytical solution.