How to use the HYPGEOM.DIST function in Excel

In this article, we will learn How to use the HYPGEOM.DIST function in Excel.

What is hypergeometric distribution ?

Hypergeometric distribution is a discrete probability distribution that describes the probability of k successes in a sample without replacement from a finite population. For example drawing 4 balls from a bag of 20 balls containing 8 white and 12 black balls. What is the probability of drawing exactly 1 white ball out of the 4 balls drawn without replacement. You must be thinking how this question is different from the normal distribution function. The problem occurs for the condition of without replacement. When we replace the drawn ball, the probability of the drawn ball remains same for each event whereas if we don't replace the ball, the probability of ball changes in the bag for each draw. Mathematically, we have a formula to calculate probability for such cases. 

Here :

N is the population size,

K is the number of success states in the population,

n is the number of draws (i.e. quantity drawn in each trial),

k is the number of observed successes,

(  ) is a combinator function expressed as n! / (k! * (n-k)!) (here ! is the factorial function)

This is still very complex to use in Excel. For this Excel provides the built in HYPGEOM.DIST function to calculate probability value in geometric distribution without replacement.

HYPGEOM.DIST Function in Excel

HYPGEOM.DIST takes the 4 numerical argument and 1 boolean value which determines the type of probability function (cdf or pdf). Let's understand these arguments one by one listed below.

HYPGEOM.DIST Function syntax:

=HYPGEOM.DIST ( sample_s , number_sample , population_s , number_pop , cumulative)

sample_s : number of successes in the sample
number_sample : sample size drawn

population_s : number of success in the population

number_pop : population size

cumulative : logical value that determines the form of the function. If cumulative is TRUE, HYPGEOM.DIST returns the cumulative distribution function; if FALSE, it returns the probability density function.


Example :

All of these might be confusing to understand. Let's understand how to use the function using an example. Here we take a regular deck of cards and we draw 4 cards from the deck without replacement. What is the probability of getting exactly 1 club card in the drawn 4 cards? Let's use the below formula to get the required probability.

Use the formula:


As you can see, there is a 0.74 or 74% (approx) probability of getting exactly 1 club card when drawing 4 cards without replacement. 

Now we can calculate the probability for drawing at least 1 club card for the same parameters just by changing the cumulative argument in the function shown below.

Use the formula:


As you can see, there is a 0.44 or 44% (approx) probability of getting at least 1 club card when drawing 4 cards without replacement. You can use the BINOM.DIST function, if drawn cards are replaced back as BINOM.DIST function works on the condition that probabilities must remain for the drawn cards.

Here are all the observational notes using the HYPGEOM.DIST function in Excel
Notes :

  1. The function only works with numbers. If any argument other than cumulative is non numeric, the function returns #VALUE! error.
  2. The function returns #NUM! Error.
    1. If sample_s value is < 0 or sample_s value > number_sample.
    2. If sample_s value > population_s value.
    3. If sample_s value > (number_sample - number_pop + population_s) value.
    4. If Number_sample value ? 0 or Number_sample > number_pop.
    5. If population_s value ? 0 or population_s > number_pop.
    6. If number_pop ? 0
  3. The cumulative argument can be used with boolean numbers (0 and 1) or (FALSE or TRUE).
  4. Value in decimal or value in percentage is the same value in Excel. Convert the value to percentage, if required.
  5. You can feed the arguments to the function directly or using the cell reference as explained in the example.

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