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Hypergeometric Distribution — result sheet
Calculate an exact and cumulative probability for successes drawn without replacement from a finite population.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: P(X=x) = C(K,x)C(N-K,n-x) / C(N,n); cumulative probability sums the feasible values from the lower support through x.
The hypergeometric model keeps the population composition fixed while drawing without replacement. K of N population members are labeled successes, n members are drawn, and the result reports the chance of exactly x successes and of at most x successes.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Population size (N) — minimum 1; maximum 1000
- Successes in population (K) — Cannot exceed the population size.; minimum 0; maximum 1000
- Sample size (n) — Draw without replacement; cannot exceed the population size.; minimum 0; maximum 1000
- Observed successes (x) — Must be feasible for the population and sample counts.; minimum 0; maximum 1000
Worked example
| Input | Value |
|---|---|
| Population size (N) | 10 |
| Successes in population (K) | 4 |
| Sample size (n) | 5 |
| Observed successes (x) | 2 |
P(X = 2) = 0.476190; P(X <= 2) = 0.738095.
Assumptions and limits
- The population has N finite members, K of which are in one success category, and the sample is a uniformly selected subset of size n.
- Every count is a whole number; x must lie between max(0, n - (N - K)) and min(n, K).
- This is a probability model for one defined sample and does not infer causation, quality, or future sampling behavior.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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