How this calculator works
P(X=k)=C(n,k)p^k(1−p)^(n−k).
Formula
P(X=k)=C(n,k)p^k(1−p)^(n−k)Calculates the probability of exactly k successes in n independent Bernoulli trials.
Worked example
Three successes in ten fair trials is a verified test case used by the calculation engine.
Assumptions and limitations
- Trials are independent.
- Each trial has the same success probability p.
- k and n are non-negative integers with k≤n.
Methodology & sources
This calculator uses deterministic, versioned calculation logic. The formula and verified examples above are part of the calculation definition used by CalcuMint. Technical calculation version: 1.
- CalcuMint deterministic statistics engine
Frequently asked questions
What does this calculator return?
It returns the probability of exactly k successes, not a cumulative probability.
Can p be zero or one?
Yes. Those deterministic boundary cases are handled explicitly.