## Hypergeometric Distribution Calculator

This calculator is used to find the probability and cumulative probabilities for Hypergeometric random variable.

Hypergeometric Distribution Calculator | |
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Population size (N): | |

No. of Successes in Population (M): | |

Sample size (n): | |

No. of Successes in sample (x): | |

Result | |

Probability : P(X = x) | |

Cumulative Probability : P(X ≤ x) | |

Cumulative Probability : P(X < x) | |

Cumulative Probability : P(X ≥ x) | |

Cumulative Probability : P(X > x) | |

## Definition of Hypergeometric Distribution

The probability mass function of hypergeometric distribution is

$$
\begin{aligned}
P(X=x) &=\frac{\binom{M}{x}\binom{N-M}{n-x}}{\binom{N}{n}},\

& \quad x=0,1,2,\cdots, n.
\end{aligned}
$$
Hypergeometric distribution gives you the probability of selecting $x$ defective units in a random sample of $n$ units out of $N$.