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Binomial probability

Find the probability of exactly k successes.

How this works

P(X=k) = C(n,k)pᵏ(1−p)ⁿ⁻ᵏ; trials must be independent with constant p.

Example

Using the example inputs, probability is 0.1171875.

Independent trials
10
Successes
3
Success probability (0–1)
0.5
Probability
0.1171875

Scope and assumptions

Extremely small probabilities may underflow to zero.

NIST statistical methods handbook

Related calculators

Poisson probability

Combinations

Factorial

Permutations

Normal interval probability

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