AllEasyToolsUniversity
Binomial probability
Binomial probability: formula, units and explained result. No account required. Processing stays in your browser.
P(X=k) = C(n,k) pᵏ (1−p)ⁿ⁻ᵏ
Independent trials with constant probability; integers 0 ≤ k ≤ n ≤ 1000.
How to use this calculator
- Identify the quantities and convert them to the units shown.
- Apply the formula first, then compare with the substitution and result.
- Check the assumptions and whether the order of magnitude makes sense.
Levels are approximate topic groupings, not a complete curriculum for every country. Numerical results are rounded and may lose precision for extreme or nearly singular inputs.
A practical example
Use these sample inputs to check the calculation before entering your own values.
- Trials n
- 10
- Successes k
- 3
- Probability p (0–1)
- 0.5
Result for this example
- Probability
- 0.11718750000000014
- Percentage
- 11.718750000000014 %