Hypergeometric Distribution

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Definition: Hypergeometric Distribution

Hypergeometric distribution function defines the probability of k successes in n attempts, all without replacement in a population of size N with maximum possible successes equal to K.

Hypergeometric distribution is a discrete probability distribution function. The population for the Hypergeometric distribution has members of only two categories. Thus, Hypergeometric distribution is similar to binomial distribution function except for the fact that in binomial distribution replacements are allowed. Hence, the probability of success changes in case of Hypergeometric distribution with each attempt.

The probability mass function of random variable X under Hypergeometric distribution is given by –

Let’s see an example on Hypergeometric Distribution:

Suppose a bag contains 30 balls (N), all of them either white or black. A success is defined by drawing a white ball. Among 30 balls, 20 balls are white (K). If 15 attempts (n) are made, what is the probability that a white ball is drawn 10 times (k)?


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