Hypergeometric Distribution Calculator

Analyze data using the hypergeometric distribution with our calculator.


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The Hypergeometric Distribution Calculator is a valuable tool for computing probabilities in a hypergeometric experiment. In statistics, the hypergeometric distribution models the probability of drawing a specific number of successes (items of interest) from a finite population without replacement. It’s commonly used in situations where the sample size is relatively small compared to the population size.

The formula for the Hypergeometric Distribution

The probability mass function of the hypergeometric distribution is defined as:

\[ P(X = k) = \frac{{\binom{K}{k} \cdot \binom{N – K}{n – k}}}{{\binom{N}{n}}} \]


  • \(P(X = k)\) is the probability of getting \(k\) successes.
  • \(K\) is the number of successes in the population.
  • \(N\) is the population size.
  • \(n\) is the sample size.
  • \(k\) is the number of successes in the sample.
  • \(\binom{n}{k}\) denotes the binomial coefficient, which can be calculated as \(\frac{n!}{k! \cdot (n – k)!}\).

Using the Calculator

This calculator allows you to:

  • Enter the values for \(K\), \(N\), \(n\), and \(k\).
  • Compute the probability \(P(X = k)\) based on the hypergeometric distribution formula.
  • Apply the hypergeometric distribution to various scenarios, such as quality control, statistical sampling, and more.


The hypergeometric distribution finds applications in a variety of fields:

  • Quality Control: Assessing the probability of defects in a sample from a production batch.
  • Statistical Sampling: Estimating the proportion of items in a population with specific characteristics.
  • Genetics: Modeling the probability of drawing individuals with specific genetic traits from a population.
  • Epidemiology: Analyzing disease outbreaks and estimating the probability of finding infected individuals.

The Hypergeometric Distribution Calculator simplifies the process of performing hypergeometric probability calculations, making it a valuable resource for statisticians, researchers, and professionals across various industries.