Please help me with this problem! Where do I even start?
The world series is a contest to determine the first of two teams to win four games. Assume that each team has an equal chance of winning any particular game and winning is independent of what happens in any other game. Find the average number of games. Give your answer as a fraction reduced to lowest terms.
There are only a few sequences of games possible. Suppose the first team wins the series. Then the possible cases are--
1. Team 1 wins all of the first 4 games
2. Team 1 wins 3 of the first 4 and then wins game 5
3. Team 1 wins 3 of the first 5 and then wins game 6
4. Team 1 wins 3 of the first 6 and then wins game 7