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.