Our hypergeometric calculator helps you quickly determine the probability of a specific number of successes in a sequence of draws from a finite population without replacement.

## Hypergeometric Probability Calculator

Use this calculator to find the hypergeometric probability based on population size, number of successes in population, sample size, and number of successes in the sample.

### How to Use the Hypergeometric Calculator

Input the following information:

- Population Size (N): The total number of items or people.
- Successes in Population (K): The number of items labeled as ‘successes’ within the population.
- Sample Size (n): The number of items you will randomly select from the population.
- Successes in Sample (k): The number of items from your sample you wish to be ‘successes’.

After inputting these values, click the “Calculate” button to get the hypergeometric probability.

### How the Calculator Works

The calculator uses the hypergeometric distribution formula to determine the probability. The formula is:

P(X = k) = [C(K, k) * C(N – K, n – k)] / C(N, n)

where C(n, k) is the combination of n items taken k at a time and P(X = k) is the probability of k successes in the sample.

### Limitations

The calculator assumes a finite population without replacement. The values for population size, successes in population, sample size, and successes in sample should be positive integers with sensible relationships (e.g., N ≥ K, n ≤ N, and k ≤ K).