The hypergeometric distribution gives the probability of a specific number of successes from a given number of draws, from a finite population, without replacement.
|-||Calculates the probability of exactly n successes from a given number of trials|
|-||Calculates the probability of at most n successes from a given number of trials|
The Excel Hypgeom.Dist function returns the value of the hypergeometric distribution for a specified number of successes from a population sample.
The function can calculate the cumulative distribution or the probability density function.
The function is new in Excel 2010, and so is not available in earlier versions of Excel. However, the probability density hypergeometric distribution can be calculated by the Hypgeomdist function, which is available in earlier versions of Excel.
The syntax of the Excel Hypgeom.Dist function is:
Where the function arguments are:
|sample_s||-||The number of successes in the sample.|
|number_sample||-||The size of the sample.|
|population_s||-||The number of successes in the population.|
|number_pop||-||The size of the population.|
|cumulative||-||A logical argument that specifies the type of distribution to be calculated. This can have the value TRUE or FALSE, meaning:|
The first four arguments to the function should all be integers. If these values are supplied as decimals, they are truncated to integers by Excel.
Imagine you have a bag, containing 3 red balls and 6 blue balls. If you remove 3 balls from the bag, the probability that 0, 1, 2 or 3 of these balls are red can be calculated by the hypergeometric distribution.
These probabilities are calculated by the Excel Hypgeom.Dist function, in cells A2-A5 of the following spreadsheet:
Note that the above example calculates the probability density function. This gives the probability of exactly sample_s successes occurring.
Imagine that you have the same bag as in Example 1, which again, contains 3 red balls and 6 blue balls.
The Excel Hypgeom.Dist function, can also be used to the calculate the probability of at most 0, 1, 2 or 3 red balls being selected from a sample of 3 balls, taken from the bag.
This is shown in the following spreadsheet:
For further examples of the Excel Hypgeom.Dist function, see the Microsoft Office website.
If you get an error from the Excel Hypgeom.Dist function this is likely to be one of the following:
|#VALUE!||-||Occurs if any of the supplied arguments are non-numeric.|