Home > Probability
| On the Brink Of Elimination (Posted on 2010-07-16) |
 |
Problem 1: In a best of 7 World Championship Series, the Mudville Nine have lost the first 3 games. What are the chances that they will rally against the Louisville Sluggers to win the next 4 games and the series, assuming the two teams are known to have an equal chance of winning any given game?
Problem 2: What are the chances that Mudville prevails if one team has a 60% chance of winning any given game? Before the series started it was equally likely that either team was the one with that advantage.
Assume that all games are played at a neutral venue, with no home field advantage. Also, there is no psychological advantage to being either on the brink of elimination, or a game away from winning the World Championship.
|
|
Submitted by Steve Herman
|
|
Rating: 3.0000 (2 votes)
|
|
|
Solution:
|
(Hide)
|
(Problem 1) 1/16
(Problem 2) The problem involves Bayesian analysis, and the final answer is less than 1/16. See Charlie's excellent first post.
By the way, major league baseball, basketball, and hockey have been playing best-of-seven series for more than 100 years in the United States, and in that time (as of May 28 2010), 287 teams have taken leads of three games to none. Only four teams (1.39%) have recovered from 3-0 to win the series. Since this is significantly less than 1/16, I conclude that either one of the teams was typically better than the other (it wasn't just chance that they were up 3-0), or that the team that was behind folded from the psychological pressure, or (more likely) both. |
Comments: (
You must be logged in to post comments.)
|
|
Please log in:
Forums (1)
Newest Problems
Random Problem
FAQ |
About This Site
Site Statistics
New Comments (10)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On
Chatterbox:
|
