Germany v Argentina World Cup Final
The FIFA officials have decided that the World Cup this year will be played as a playoff series between Germany and Argentina.
The series will be played one game at a time until one team has won 4 games. (at which time the series is over.)
In each game, Germany has a 70% chance of winning and Argentina a 30% chance.
What is the probability that the World Cup series lasts for 7 games?
The answer is 0.18522.
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1 solution
For the series to last 7 games means one team has to win 3 out of 6 games in any order and then go on to win the 7th game.
That's 6C3 (0.7)^4 (0.3)^3 + 6C3 (0.3)^4 (0.7)^3 = 0.18522