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Formula verified · Deterministic calculation

Binomial Probability Calculator

Enter the number of trials, target successes and per-trial success probability to evaluate the binomial probability mass function.

P(X = k)0.1171875
Trials (n)10
Successes (k)3
Success probability0.5
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Result methodology

Exact-k binomial probability for independent Bernoulli trials with constant success probability.

Solution steps
  1. n = 10; k = 3; p = 0.5
  2. P(X=k) = C(n,k)p^k(1-p)^(n-k) = 0.11718750000000014

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.

  • 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.

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