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Let's say we bet on 10 different soccer matches. The probability of our team winning, for each game, is 0.17, 0.78, 0.41, 0.79, 0.47, 0.08, 0.29, 0.30, 0.35, and 0.54. What is the probability of winning at least 3 of these bets?

I know how to deal with this problem when the probability of each event is the same (coin tosses etc), but get confused when they are different.

miroli
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    This is called the poisson-binomial distribution https://en.wikipedia.org/wiki/Poisson_binomial_distribution . There is an R package `poisbinom` on CRAN. – kjetil b halvorsen Oct 27 '17 at 13:52

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