The page will calculate the following: Exact binomial probabilities, Approximation via the normal distribution, Approximation via the Poisson Distribution. This page will calculate and/or estimate binomial probabilities for situations of the general "k out of n" type, where k is the number of times a binomial outcome is observed or stipulated to occur, p is the probability that the outcome will occur on any particular occasion, q is the complementary probability (1-p) that the outcome will not occur on any particular occasion, and n is the number of occasions.
An application of Bayes Theorem that performs the same calculations for the situation where the several probabilities are constructed as indices of subjective confidence.
This page will generate a graphic and numerical display of the properties of a binomial sampling distribution, for any values of p and q, and for values of n between 1 and 40, inclusive.