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I have a dataframe that contains formula 1 drivers, the season, the round, as well as variables for the probability that they finish in a specific position (Probability_predictions.1 through Probabilities_predictions.20). I'm trying get the probability of one driver finishing ahead of the other driver which would be done using this formula : P(A<B) = P(A=1)\*P(B>1) + P(A=2)*P(B>2) + P(A=3)*P(B>3) + ... + P(A=18)*P(B>18)+P(A=19)*P(B>19).

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