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.
(In reply to Solution
But the fact that Mudville already lost the first three games is evidence that, now, it's less likely to be the team with the higher probability of winning a game.
Posted by Charlie
on 2010-07-19 12:14:51