Binomial Probability

Calculate the exact probability of a number of successes in independent Bernoulli trials.

How this calculator works

Enter number of trials, exact successes, success probability. CalcStack applies the displayed formula and reports each intermediate planning value with the units shown.

Formula / method

P(X=k) = C(n,k)p^k(1−p)^(n−k)

Worked example

Exactly 8 successes in 20 trials with p=0.4 has probability about 0.1797.

Assumptions and limitations

Trials are independent with constant success probability.

This does not calculate cumulative probability and is unsuitable for dependent trials.