# Documentation/Calc Functions/HYPGEOM.DIST

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## Function name:

HYPGEOM.DIST

## Category:

Statistical Analysis

## Summary:

Calculates values from either the probability mass function or the cumulative distribution function for the hypergeometric distribution of a sequence. The hypergeometric distribution is a discrete probability distribution that describes the probability of a particular number of successes in a sequence of draws from a finite population without replacement.

## Syntax:

HYPGEOM.DIST(**X**; **NSample**; **Successes**; **NPopulation**; **Cumulative**)

## Returns:

Returns a real number which is the hypergeometric distribution value for the given arguments. It ranges from 0 to 1, i.e. [0,1].

## Arguments:

**X** is a non-negative integer value or a reference to the cell containing that value which is the number of successes achieved in the random sample.

**NSample** is a non-negative integer value or a reference to the cell containing that value which is the size of the random sample.

**Successes** is a non-negative integer value or a reference to the cell containing that value which is the number of possible successes in the total population.

**NPopulation** is a non-negative integer value or a reference to the cell containing that value which is the size of the total population.

**Cumulative** specifies whether to calculate the probability density function (FALSE or 0) or the cumulative distribution function (any other value).

- Given arguments must satisfy both these conditions:

0 <= X <= NSample <= NPopulation

0 <= Successes <= NPopulation

or else the function will return an error value.

## Additional details:

The formula for HYPGEOM.DIST is:

If Cumulative is FALSE(), HYPGEOM.DIST returns the probability mass function value

If Cumulative is TRUE(), HYPGEOM.DIST returns the cumulative distribution function

where:

is COMBIN(n,x)

x = **X**
n = **NSample**
M = **Successes**
N = **NPopulation**

- For more details about the hypergeometric distribution, visit Wikipedia.

## Examples:

Formula | Description | Returns |
---|---|---|

=HYPGEOM.DIST(2;2;90;100) | If 90 out of 100 pieces of buttered toast fall from the table and hit the floor with the buttered side first, then if 2 pieces of buttered toast are dropped from the table, the probability is around 81%, that both will strike buttered side first. Here no value for Cumulative is mentioned hence the function calculates probability mass function. |
0.809090909090909 |

=HYPGEOM.DIST(15;30;90;150;TRUE()) | The function calculates the cumulative distribution function for the hypergeometric distribution. | 0.148888209892056 |

=HYPGEOM.DIST(15;13;90;150;TRUE()) | NSample value is less than X hence the function returns an error value. |
Err:502 |

## Related LibreOffice functions:

## ODF standard:

None

## Equivalent Excel functions:

HYPGEOM.DIST