Analytical Geometry

Hypergeometric distribution formula


Population size ( The total number of items in the population):

Number of successes in population :
Sample size (The total number of items selected from the population):
Number of success in sample :
  • Τhe hypergeometric distribution is a discrete probability distribution that describes the number of successes in a sequence of n draws from a finite population without replacement
  • Suppose you are to draw "n" balls without replacement from an basket containing "N" balls in total, "m" of which are white. The hypergeometric distribution describes the distribution of the number of white marbles drawn from the urn.
  • A random variable X follows the hypergeometric distribution with parameters N, m and n andf the probability is given by :

For example, Think an basket wich contains two types of balls, blacks and whites. Define drawing a white ball as a success and drawing a black ball as a failure (analogous to the binomial distribution). If the variable N describes the number of all balls in the basket and m describes the number of white marbles, then N − m corresponds to the number of black balls.
Now, assume (for example) that there are 5 white and 45 black balls in the basket. Close your eyes and draw 10 balls without replacement.

What is the probability that exactly 4 of the 10 are white?

  • N=50, m=5, n=10, k=4

The probability is :




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