HYPGEOMDIST

Calculates values for a hypergeometric distribution.

Syntax:

HYPGEOMDIST(x, n, M, N)

The hypergeometric distribution is a discrete probability distribution giving the probability of x successes in a sequence of n draws (without replacement) from a finite population of size N which contains M successes.

HYPGEOMDIST calculates the probability density function of the hypergeometric distribution:

$\frac{n u mb er _ w a ys _ f or _ x _ s u ccesses \times n u mb er _ w a ys _ f or _ ( n - x ) _ f ai l u res}{t o t a l _ n u mb er _ o f _ w a ys _ t o _ se l ec t}$

which is

$\frac{( M x ) ( N - M n - x )}{( N n )}$

Example:

HYPGEOMDIST(2, 3, 3, 6)

returns 0.45. If an urn contains 3 red balls and 3 green balls, the probability that 2 red balls will be selected after 3 draws without replacement is 27/60 = 0.45.

Application:

Imagine a quality control scenario in a factory. You have a batch of 50 circuit boards, and you know from past experience that 5 of them are defective. You randomly select 10 circuit boards from the batch to test. You want to know the probability of finding exactly 2 defective circuit boards in your sample.

This is an application of using the HYPGEOMDIST function, which calculates the probability of a given number of successes in a sample drawn without replacement from a finite population.

Here's how the values would break down for the HYPGEOMDIST function:

	Parameter	Value	Description
	A	B	C
1	Sample_S	2	The number of successes in the sample (the number of defective boards you want to find).
2	Number_sample	10	The size of the sample (the number of boards you are testing).
3	Population_S	5	The number of successes in the population (the total number of defective boards in the batch).
4	Number_population	50	The total size of the population (the total number of boards in the batch).

The HYPGEOMDIST function would then be used as follows:

HYPGEOMDIST(2, 10, 5, 50)

This would return the probability of finding exactly 2 defective circuit boards in your sample of 10. The result is approximately 0.2098, or 20.98%. This means there is a 20.98% chance that you will find exactly two defective boards in your random sample.

Result for HYPGEOMDIST(2, 10, 5, 50):

0.2098