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.