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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?

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I am afraid it is not because the chance of corners and goals are most likely correlated (3 corners 1 goal, I think is the saying).

If corner and goal are highly correlated, then the information that a team got 2 goals doesn't tell us much more about its win probability after we already know that they have 6 corners. For perfect correlation actually P(6 corners) = P(6 corners and 2 goals) = 0.6.

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).

But as we don't know the correlation between corners and goals, we cannot say which of these two (or any probabilities in between) is true. Thus my answer is that it is not possible.

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