# 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:

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

Where:

- \(P(X = k)\) 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.

## Applications

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.