# Combining probabilities from multiple observations

Given a number of probabilities taken from a large number of recorded football games.

• A: Chance of WIN given 6 corners: 0.6
• B: Chance of WIN given 2 goals: 0.6
• C: Chance of LOSS given 2 red cards: 0.7

Is it possible to calculate an estimate for the chance of a WIN given 6 corners, 2 goals and 2 red cards?

For the completely uncorrelated case P(6 corners and 2 goals) = $$1 - (1-0.6)^2 =0.84$$ (basically a Bernoulli trial with two draws).