Formulas and functions > Functions from A to Z > BINOMDIST (binomial distribution)

Note: BINOMDIST is supplemented by the new identical function BINOM.DIST and the completely new function BINOM.DIST.RANGE, which are available in newer versions of Microsoft Excel (2010 or later).

Syntax:

BINOMDIST(k, n, p, Cumulative)

Description:

This returns the binomial distribution function.

The binomial distribution can be used to determine the probability of obtaining k successes in an experiment with n independent trials with only two possible outcomes (success or failure) with a fixed probability of p for each trial.

For example, you can use this function to determine the probability of obtaining "heads" exactly 4 times if you toss a coin 10 times.

k is the number of successes, thus 4 here. It must be within the range 0 to n.

n is the number of independent trial runs, thus 10 here.

n and k should be integers. If this is not the case, PlanMaker automatically truncates the decimal places.

p is the probability of the success of each trial run, for example, the probability of obtaining "heads" here, i.e., 50%.

You use the logical value Cumulative to specify which type of function will be returned:

FALSE: The probability density function is returned. BINOMDIST thus determines the probability of having exactly k successes.

TRUE: The cumulative distribution function is returned. BINOMDIST thus determines the probability that there are at most k successes.

Example:

Let's take the above example:

When you toss a coin 10 times (n=10), what is the probability of it landing on "heads" (p=50%) exactly 4 times?

BINOMDIST(4, 10, 50%, FALSE) returns 0.20508 =20.5%

What is the probability of it landing on "heads" 4 times at most?

Instead of the density function, you use the distribution function (specify the Cumulative argument with TRUE):

BINOMDIST(4, 10, 50%, TRUE) returns 0.37695 =37.7%