Statistics & Probability Calculators
Binomial Probability Calculator
Compute P(X = k) for a binomial distribution with n trials and probability p.
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What is Binomial Probability?
A binomial distribution counts successes in n independent trials that each succeed with probability p. Its probability mass function is P(X = k) = nCk · pᵏ · (1 − p)ⁿ⁻ᵏ, and its mean is np.
How it works
The binomial coefficient and the two powers are combined in log space, so large n does not overflow the intermediate count, and the cumulative forms are summed from the same terms. All three probabilities are shown because exam questions ask for "at least" and "at most" at least as often as "exactly".
- Enter your input. Type or paste your input into the field above — the tool responds instantly.
- Review the result. Output updates live as you type. Everything runs entirely in your browser.
- Copy or download. Use the Copy button to grab the result, or Download to save it as a file.
Examples
Realistic sample
Type or paste any realistic input — the tool computes the result locally and instantly.
Common mistakes
Expecting a server round-trip
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