Let's say I'm playing 10 "games". For each game, I know the probability of winning, the probability of tying, and the probability of losing.
From these values, I can calculate the probability of winning X games, the probability of losing X games, and the probability of tying X games (for X = 0 to 10).
I'm just trying to figure out the probability of each outcome after playing all 10 games. For example, what is the probability of winning 7, losing 2, and tying 1?
Any ideas? Thanks!
Here's some example data for 2 games:
Game 1:
- win: 23.3%
- tie: 1.1%
- lose: 75.6%
Game 2:
- win: 29.5%
- tie: 3.2%
- lose: 67.3%
Based on this, we can calculate the probability after playing 2 games of:
- 0 wins: 54.0%
- 1 win: 39.1%
- 2 wins: 6.9%
- 0 ties: 95.8%
- 1 tie: 4.2%
- 2 ties: 0.0%
- 0 losses: 8.0%
- 1 loss: 41.1%
- 2 losses: 50.9%
Based on these numbers, what is the probability of each outcome? The possible outcomes (W-L-T) would be:
- 2-0-0
- 1-1-0
- 1-0-1
- 0-1-1
- 0-2-0
- 0-0-2
Obviously this is pretty trivial with 2 games, but is there a generic formula for finding the probability of W wins, T ties, and L losses after X games?