HyperGeometric Command
 HyperGeometric( <Population Size>, <Number of Successes>, <Sample Size>)

Returns a Hypergeometric distribution bar graph.
Parameters:

Population size: number of balls in an urn

Number of Successes: number of white balls in the urn

Sample Size: number of balls drawn from the urn
A random sample is repeatedly extracted from an urn, without replacement. HyperGeometric(100, 50, 5)
generates a bar graph showing the probability distribution of the number of white balls in the sample.
 HyperGeometric( <Population Size>, <Number of Successes>, <Sample Size>, <Boolean Cumulative> )

When Cumulative = false returns a bar graph of a Hypergeometric distribution, otherwise it returns the graph of a cumulative Hypergeometric distribution function. 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. The first three parameters are same as above.

When Cumulative = false it returns P( X = v)

When Cumulative = true it returns P( X ≤ v)

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.
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. The first three parameters are the same as above.

When Cumulative = false it returns P( X = v)

When Cumulative = true it returns P( X ≤ v)
