I am searching the name of something similar to a binomial distribution, but with individual probabilities (P(1) to P(N)).
I calculated (brute-forced with a script) the probability of k positive outcomes of N binary events of known (different) probabilities the following way:
Once N individual probabilities (for N binary events) were estimated, the exact probability of k observed positive outcomes in a distribution of all N+1 possible combined outcomes (totals), was calculated as the sum over all possible binary combinations (2N) with outcome k, each multiplied by the product of all N individual probabilities of the combined outcome.
Does this 'algorithm' have a name? How would this be written as a formula?
I am searching for something like: Probability of outcome K = Formula
