Hypergeometric Distribution Calculator

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

Hypergeometric Distribution Calculator
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 $N$.

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