Hypergeometric Distribution Calculator

Calculate probabilities for sampling without replacement using the hypergeometric distribution.

Distribution Parameters

Population Size (N)*

The total number of items in the population

Number of Success States in Population (K)*

The number of items in the population that are classified as successes

Sample Size (n)*

The number of items drawn from the population without replacement

Select Probability Type

Number of Successes in Sample (k)*

The number of success states in the sample

The probability mass function of the hypergeometric distribution is:

P(X = k) = \frac{\binom{K}{k} \binom{N-K}{n-k}}{\binom{N}{n}}

Where:

The binomial coefficient is calculated as:

\binom{n}{k} = \frac{n!}{k!(n-k)!}

Mean (μ): n × (K/N) = 4.0000

Variance (σ²): n × (K/N) × ((N-K)/N) × ((N-n)/(N-1)) =1.9592

Standard Deviation (σ): √(Variance) =1.3997

Work with the normal probability distribution.

Calculate binomial probabilities.

Work with the Poisson probability distribution.