What you provide
What you provide
- Number of trials, using the same scenario as the other inputs
- Number of successes, using the same scenario as the other inputs
- Success probability, using the same scenario as the other inputs
MATH / PROBABILITY
Binomial Probability Calculator
Calculate the probability of exactly k successes across independent Bernoulli trials. Review the equation, substituted values, result context, and modelling limits in one guided workspace.
- 01 Calculated in this tab
- 02 Values stay in this browser tab
- 03 Use boundary
Use boundary
Calculation path
Calculate the probability of exactly k successes across independent Bernoulli trials. The page evaluates the displayed equation from your supplied values and presents both symbolic and substituted KaTeX working so the arithmetic can be checked.
Calculation path
P(X=k) = C(n,k)p^k(1-p)^(n-k)
What you receive
What you receive
- Exact-outcome probability from the stated equation
- A symbolic formula plus substituted working with your values
- Visible assumptions, field guidance, and an authoritative learning reference
Use boundary
Choose the maximum decimal places shown. This does not increase source accuracy.
Trials must be independent with one constant success probability.
Use internally consistent units and retain extra precision when carrying the result into another calculation.
Reviewed reference factors