Suppose that two sports teams were to play each other in a series, and the winning team is the one that wins two games. One of the teams, Team A, has a probability of 80% chance of winning any one game. What is the probability of Team A winning the series?
The answer that I reached is 64%, and my reasoning is that for Team A to win, there must be two conditions:
- Team A must win its first game
- Team A must win its second game
With that in mind, I multiplied 80% (the chance of Team A winning its first game) with 80% again (because it has 80% chance of winning its second game). Is this correct? I'm getting a bit tripped up because the probability of Team A winning its second game is not dependent on its probability of winning the first game, so that's why I'm sort of leaning on the total probability being 80% again (because if we can assume Team A wins its first game then everything else is irrelevant; the chances of them winning again is 80%).