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Suppose there are 9 events, that have a probability of 10%, 20%, 30%, ..., 90% of being a success.

How would I find the probability of exactly n number of these events succeeding?

For n = 1, I'm thinking it is something like

(first succeeds) -> (1-0.9) * 0.8 * 0.7 * 0.6 ... 0.1 (second succeeds) -> 0.9 * (1-0.8) * 0.7 * 0.6 ... 0.1 (...) (last) 

and then adding them up.

The probabilities might not always be an an Arithmetic Progression, hoping to find a solution that doesn't depend on that.

3 Answers 3