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Let's say that I know the probability of a "success" is P. I run the test N times, and I see S successes. The test is akin to tossing an unevenly weighted coin (perhaps heads is a success, tails is a failure). I want to know the approximate probability of seeing either S successes, or a number of successes less likely than S successes. So for example, if P is 0.3, N is 100, and I get 20 successes, I'm looking for the probability of getting 20 or fewer successes. If, on the other hadn, P is 0.3, N is 100, and I get 40 successes, I'm looking for the probability of getting 40 our more successes. I'm aware that this problem relates to finding the area under a binomial curve, however: My math-fu is not up to the task of translating this knowledge into efficient code While I understand a binomial curve would give an exact result, I get the impression that it would be inherently inefficient. A fast method to calculate an approximate result would suffice. I should stress that this computation has to be fast, and should ideally be determinable with standard 64 or 128 bit floating point computation. I'm looking for a function that takes P, S, and N - and returns a probability. As I'm more familiar with code than mathematical notation, I'd prefer that any answers employ pseudo-code or code.

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