Binomial Probability
Find the chance of exactly k successes in n independent trials.
Your numbers
Exactly k successes
Use consistent units. The result follows the assumptions you enter.
Scenario comparison
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Formula
P(X=k)=C(n,k)pᵏ(1−p)ⁿ⁻ᵏ
Find the chance of exactly k successes in n independent trials.
Worked example
- Trials n
- 10
- Successes k
- 3
- Success probability (%)
- 50
- Exactly k successes
- 11.71875 %
Scope and limitations
Use consistent units. The result follows the assumptions you enter.
Inputs are checked for missing values and allowed ranges. A result outside the finite numeric range is not displayed. Rounding affects display, while the calculation uses the model’s numeric precision.
Check your units and assumptions before relying on a result. Changing a label does not convert a currency or physical unit.
Formula version: 4050b488d999 · Example checked: