Result
Enter values and select Calculate.
Formula and method
For exactly x successes, P(X=x) = C(n,x)pˣ(1−p)ⁿ⁻ˣ. The engine evaluates the PMF in log space and cumulative tails with the regularized incomplete beta function, avoiding direct factorial overflow. Boundary distributions at p = 0, p = 1, and n = 0 are handled exactly.
Worked example
For 10 trials, p = 0.5, and exactly 5 successes, the probability is 0.24609375. The mean is 5 and variance is 2.5.
Assumptions and boundaries
- Trials are independent, each trial has two modeled outcomes, and p stays constant.
- n and success counts are integers; 0 ≤ p ≤ 1 and 0 ≤ x ≤ n.
- n is limited to 10,000 for responsive browser-local computation.
- This page uses combinations internally; Combination Calculator retains nCr ownership.
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