Hypergeometric Probability Calculator
Calculate successes in sampling without replacement from a finite population.
Loading tool…
How to use Hypergeometric Probability Calculator
Hypergeometric weights use C(K,k)×C(N−K,n−k)/C(N,n). Log-combination weights are normalized over the feasible support before summing either tail.
- Enter population n, population successes k, sample draws n, observed successes k.
- Check the model, units, and supported limits before calculating.
- Run the tool, inspect the result, then copy or download it.
Good to know
- Whole population 1–10000; successes and draws within that population. Count 0–10000. Uniform sampling without replacement is required; values outside feasible support have zero mass.
- Runs locally. Numeric inputs are bounded; floating-point output is approximate and rounded to 12 significant digits. Unsupported or non-finite calculations produce an error.
Common questions
How does Hypergeometric Probability Calculator calculate its result?
Hypergeometric weights use C(K,k)×C(N−K,n−k)/C(N,n). Log-combination weights are normalized over the feasible support before summing either tail.
What assumptions and boundaries apply?
Whole population 1–10000; successes and draws within that population. Count 0–10000. Uniform sampling without replacement is required; values outside feasible support have zero mass.
Keep going with related tools
All math →Poisson Probability Calculator
Evaluate an event-count probability and both cumulative tails for a supplied expected count.
MathBinomial Probability Calculator
Find exact-count and cumulative probabilities for independent trials with a fixed success chance.
MathCombinations and Permutations Calculator
Count selections and ordered arrangements without repetition using exact integer arithmetic.
CalculatorsFinite-lot Acceptance Plan Workbench
Find a bounded single-sample plan that meets two explicit finite-lot defective-count risk limits.
MathFisher Exact2×2 Test Calculator
Compute a bounded fixed-margin Fisher exact probability with a named one- or two-sided alternative.
MathChi-square Independence Calculator
Inspect a two-way count table with Pearson’s statistic, expected counts, and a conditional approximate p value.