# Hypergeometric Distribution Calculator

Analyze data using the hypergeometric distribution with our calculator.

 Population Size Number of Success in Population Sample Size Number of Success in Sample
 Result: Hypergeometric Distribution Cumulative Hypergeometric Distribution

## Similar Calculators:

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.