The Excel BINOM.DIST Function

Related Functions:

BINOM.DIST.RANGE
BINOM.INV
NEGBINOM.DIST

BINOMIAL DISTRIBUTION

The Binomial Distribution is a statistical measure that is frequently used to indicate the probability of a specific number of successes occurring from a specific number of independent trials.

The following two forms are used:

The Probability Mass Function - calculates the probability of there being exactly x successes from n independent trials
The Cumulative Distribution Function - calculates the probability of there being at most x successes from n independent trials

Further information can be found on the Wikipedia Binomial Distribution page

Function Description

The Excel BINOM.DIST function returns the Binomial Distribution probability for a given number of successes from a specified number of trials.

The function is new in Excel 2010 and so is not available in earlier versions of Excel. However, the Binom.Dist function is simply an updated version of the Binomdist function that is available in earlier versions of Excel.

The syntax of the Binom.Dist function is:

BINOM.DIST( number_s, trials, probability_s, cumulative )

where the arguments are:

number_s

The number of successes that you want to calculate the probability for.

trials

The number of independent trials that are to be done.

probability_s

The probability of success in one trial.

cumulative

A logical argument that specifies the type of Binomial distribution to be calculated. This can have the value TRUE or FALSE meaning:

TRUE	-	use the cumulative distribution function;
FALSE	-	use the probability mass function.

Note that, if decimal values are input for the number_s or trials arguments, these are truncated to integers by Excel.

Binom.Dist Function Example 1

Binomial Distribution Probability Mass Function Chart

Probability Mass Function for 100 Tosses of a Coin

The above chart on the right uses the Binomial Distribution Probability Mass Function to show the probability that exactly x heads will be thrown from 100 tosses of a coin.

In column A of the spreadsheet below, the Excel Binom.Dist function is used to evaluate this function for three different values of x.

Clearly, the probability of tossing a head on any one trial is 0.5, so this is input as the value of the probability_s argument in each case.

Formulas:

	A
1	=BINOM.DIST( 10, 100, 0.5, FALSE )
2	=BINOM.DIST( 50, 100, 0.5, FALSE )
3	=BINOM.DIST( 65, 100, 0.5, FALSE )

Results:

	A	B
1	1.36554E-17	- probability of exactly 10 heads
2	0.079589237	- probability of exactly 50 heads
3	0.000863856	- probability of exactly 65 heads

Binom.Dist Function Example 2

Binomial Cumulative Distribution Function Chart

Cumulative Distribution Function for 100 Tosses of a Coin

The above chart on the right shows the Binomial Cumulative Distribution Function for the probability of throwing at most x heads from 100 tosses of a coin.

In column A of the spreadsheet below, the Excel Binom.Dist function is used to evaluate this function for three different values of x.

Again, the probability of tossing a head on any one trial is 0.5, so this is input as the value of the probability_s argument.

Formulas:

	A
1	=BINOM.DIST( 10, 100, 0.5, TRUE )
2	=BINOM.DIST( 50, 100, 0.5, TRUE )
3	=BINOM.DIST( 65, 100, 0.5, TRUE )

Results:

	A	B
1	1.53165E-17	- probability of at most 10 heads
2	0.539794619	- probability of at most 50 heads
3	0.999105035	- probability of at most 65 heads

For further examples of the Excel Binom.Dist function, see the Microsoft Office website.

Binom.Dist Function Errors

If you get an error from the Excel Binom.Dist Function, this is likely to be one of the following:

Common Errors

#NUM!

Occurs if either:

The supplied number_s is < 0 or > trials;
The supplied probability_s is < 0 or > 1.

#VALUE!

Occurs if any of the number_s, trials, or probability_s arguments are non-numeric.

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