# HyperGeometric Command

From GeoGebra Manual

- HyperGeometric( <Population Size>, <Number of Successes>, <Sample Size>)
- Returns a bar graph of a Hypergeometric distribution.
*Parameters:**Population size*: number of balls in the urn*Number of Successes*: number of white balls in the urn*Sample Size*: number of balls drawn from the urn

The bar graph shows the probability function of the number of white balls in the sample.

- HyperGeometric( <Population Size>, <Number of Successes>, <Sample Size>, <Boolean Cumulative> )
- Returns a bar graph of a Hypergeometric distribution when
*Cumulative*= false. - Returns the graph of a cumulative Hypergeometric distribution when
*Cumulative*= true. - First three parameters are same as above.

- HyperGeometric( <Population Size>, <Number of Successes>, <Sample Size>, <Variable Value>, <Boolean Cumulative> )
- Let X be a Hypergeometric random variable and v the variable value.
- Returns P( X =
*v*) when*Cumulative*= false. - Returns P( X ≤
*v*) when*Cumulative*= true. - First three parameters are same as above.

## CAS Syntax

In the CAS View you can use only the following syntax:

- HyperGeometric( <Population Size>, <Number of Successes>, <Sample Size>, <Variable Value>, <Boolean Cumulative> )
- Let X be a Hypergeometric random variable and v the variable value.
- Returns P( X =
*v*) when*Cumulative*= false. - Returns P( X ≤
*v*) when*Cumulative*= true. - The first three parameters are the same as above.
**Example:**Assume you select two balls out of ten balls, two of which are white, without putting any back.`HyperGeometric(10, 2, 2, 0, false)`

yields \frac{28}{45}, the probability of selecting zero white balls,`HyperGeometric(10, 2, 2, 1, false)`

yields \frac{16}{45}, the probability of selecting one white ball,`HyperGeometric(10, 2, 2, 2, false)`

yields \frac{1}{45}, the probability of selecting both white balls,`HyperGeometric(10, 2, 2, 3, false)`

yields*0*, the probability of selecting three white balls.`HyperGeometric(10, 2, 2, 0, true)`

yields \frac{28}{45}, the probability of selecting zero (or less) white balls,`HyperGeometric(10, 2, 2, 1, true)`

yields \frac{44}{45}, the probability of selecting one or less white balls,`HyperGeometric(10, 2, 2, 2, true)`

yields*1*, the probability of selecting two or less white balls and`HyperGeometric(10, 2, 2, 3, true)`

yields*1*, the probability of selecting three or less white balls.