# Manuals/calci/HYPGEOMDIST

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HYPGEOMDIST (sample_s,number_sample,population_s,number_population,cumulative)

• is the sample's success.
• is the sample's size.
• is population's success.
• is the population size.
• HYPGEOMDIST(),returns the hypergeometric distribution.

## Description

• This function gives the result of Hypergeometric Distribution.
• This distribution is a discrete probability distribution which is contrast to the binomial distribution.
• A Hypergeometric random variable is the number of successes that result from a Hypergeometric experiment.
• The probability distribution of a Hypergeometric random variable is called a Hypergeometric Distribution.
• In HYPGEOMDIST (sample_s,number_sample,population_s,number_population,cumulative) where samples is the number of items in the Sample that are classified as successes.
•   is the total number of items in the sample.
•   is the number of items in the population that are classified as successes and   is the total number of items in the sample.
• The following conditions are applied to the Hypergeometric distribution:
1.This distribution is applies to sampling without replacement from a finite population whose elements can be
classified into two categories like Success or Failure.
2.The population or set to be sampled consists of N individuals, objects,or elements
3.Each individual can be  success (S) or a failure (F), and there are M successes in the population.
4.A sample of individuals is selected without replacement in such a way that each subset of
size is equally likely to be chosen.

• The Hyper geometric probability distribution is:

for   is an integer satisfying  . where   is sample's success.

•   is the sample's size.
•   is population's success and   is the population size.
• Here we can give any positive real numbers.
• Suppose we are assigning any decimals numbers it will change in to Integers.
• This function will give result as error when
1.Any one of the argument is non-numeric.
2. or samples is greater than the smaller value of numbersample or populations.
3. is less than the bigger of 0 or(numbersample-numberpopulation+populations)
4. or 5. or or ## ZOS

• The syntax is to calculate HYPGEOMDIST in ZOS is
•   is the sample's success.
•   is the sample's size.
•   is population's success.
•   is the population size.
• For e.g.,HYPGEOMDIST(2..3,6..7,9..10,20)
Hyper-geometric Distribution

## Examples

1. Draw 6 cards from a deck without replacement.What is the probability of getting two hearts?
Here M = 13 number of hearts
N = 52 total number of cards
so N-M= 52-13= 39 and
x=2,n=6 so n-x=6-2=4
=HYPGEOMDIST(2,6,13,52)=0.315129882

1. 42 balls are numbered 1 - 42.You select six numbers between 1 and 42. What is the probability that they contain (i)match 3, (ii) match 4
(i)Here M= 6,N=42,x=3and n=6
HYPGEOMDIST(3,6,6,42)=0.02722185
(ii)Here M= 6,N=42,x=4and n=6
HYPGEOMDIST(4,6,6,42)=0.001801446


## Related Videos

Hyper-Geometric Distribution