Manuals/calci/HYPGEOMDIST

HYPGEOMDIST(n1,n2,n3,n4)

• $n1$ is the sample's success.
• $n2$ is the sample's size.
• $n3$ is population's success.
• $n4$ is the population size.

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(n1,n2,n3,n4) where n1 is the number of items in the Sample that are classified as successes.
• $n2$ is the total number of items in the sample.
• $n3$ is the number of items in the population that are classified as successes and $n4$ 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 $n$ individuals is selected without replacement in such a way that each subset of 
  size $n$ is equally likely to be chosen.

• The Hyper geometric probability distribution is:

${\frac {{\binom {m}{x}}{\binom {N-M}{n-x}}}{\binom {m}{x}}}$ for Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x} is an integer satisfying Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle max(0, n-N+M)<=x<=min(n,M)} . where Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x} is sample's success.

• Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle n} is the sample's size.
• Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle M} is population's success and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle N} 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.Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle n1 < 0}
 or n1 is greater than the smaller value of n2 or n3.
3.Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle n1}
 is less than the bigger of 0 or(n2-n4+n3)
4.Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle n2 \le 0}
 or Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle n2>n4}

5.Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle n3 \le 0}
 or  Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle n3>n4}
 or Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle n4 \le 0}

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

See Also

• BINOMDIST
• COMBIN
• FACT

References

Hypergeometric Distribution