HyperGeometric Command

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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 Menu view cas.svg 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 \mathrm{\mathsf{ \frac{28}{45} }}, the probability of selecting zero white balls,
  • HyperGeometric[10, 2, 2, 1, false] yields \mathrm{\mathsf{ \frac{16}{45} }}, the probability of selecting one white ball,
  • HyperGeometric[10, 2, 2, 2, false] yields \mathrm{\mathsf{ \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 \mathrm{\mathsf{ \frac{28}{45} }}, the probability of selecting zero (or less) white balls,
  • HyperGeometric[10, 2, 2, 1, true] yields \mathrm{\mathsf{ \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.
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