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Hypergeometric Distribution Tutorial

  


Definition:

   In statistics, hypergeometric distribution is one of the discrete probability distribution. This distribution is used for calculating the probability for a random selection of an object without repetition. Here, population size is the total number of objects in the experiment.

Formula:

  h(x;N;n;k) = [kCx] [N-kCn-x] / [NCn]
  where,
  N is the total population size.
  n is the total sample size.
  k is the number of selected items from the population size.
  x is a random variable.

Example:

  Consider, 5 balls are chosen randomly from the total of 10 balls without repetition. Calculate the probability of getting exactly 2 red balls out of 6 red balls.

 Step1:Find [kCx]

 where,   N=10, n=6, k=5 and x=2

 [kCx] = ( k! / (k-x)!) / x!
         = (5! / (5-2)!) / 2! = 20 / 2 = 10.

 Step2: Find [N-kCn-x]

 where, N-k=5 and n-x=4

 [N-kCn-x] = ((N-k)! / ((N-k)-(n-x))!) / (n-x)!
             = ((5! / 1!) / 4!) = 5 / 4! = 5.

 Step3: Find [NCn]

 where,  N=10 and n=6

 [NCn] = ( N! / (N-n)!) / n!)
         = ((10! / 4!) / 6!) = 151200 / 6! = 210.

 Step4: Find [kCx] [N-kCn-x] / [NCn]

 where,

 [kCx] = 10, [N-kCn-x] = 5 and [NCn] = 210.

 h(x;N;n;k) = [kCx] [N-kCn-x] / [NCn]
                = [5C2] [5C4] / [10C6]
                = (10 x 5) / 210
                = 0.238.

 Hence there are 23.8% possibilities for choosing exactly 2 red balls without repetition.



This tutorial will guide you to calculate the hypergeometric distribution problems.

Related Topics:
>> What is Cumulative Hypergeometric distribution?

Related Calculator:
>> Calculate Hypergeometric Distribution online