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Excel BINOM.DIST function

The BINOM.DIST function returns the individual term binominal distribution probability, which can be used to calculate the probability of a specified number of successes out of a given number of trials.

Syntax

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

Arguments

  • Number_s (required): The number of successes in trials;
  • Trials (required): The number of independent trials;
  • Probability_s (required): The probability of success per trial;
  • Cumulative (required): A logical value used to determine the form of the function. It can be:
-- TRUE: use the cumulative distribution function;
-- FLASE: use the probability mass function.

Remarks

1. If the arguments “number_s” and “trials” are not integers, they will be truncated;
2. The #NUM! error value occurs when any of the following conditions is met:
-- “Number_s” < 0;
-- “Number_s” > “trials”;
-- “Probability_s” < 0, or “Probability_s” > 1;
3. The #VALUE! error value occurs if any of the supplied “number_s”, “trials” or “probability_s” are non-numeric;
4. Supposing x = number_s, n = trials, and p = probability_s, the equations for the cumulative distribution function and the probability mass function are as follows:
-- The equation for the cumulative distribution function:
-- The equation for the probability mass function:
where:
is COMBIN(n,x).

Return value

It returns a numeric value.

Example

As shown in the table below, there are 6 successes in 14 trials, and the probability of success in each trial is 0.5. To calculate the probability of at most 6 successes out of 14 trials and the probability of 6 successes out of 14 trials separately, you can apply the BINOM.DIST function as follows.

1. Calculate the probability of exactly 6 successes out of 14 trials.

Select a cell (E6 in this case), copy or enter the formula below and press Enter to get the result.

=BINOM.DIST(B6,C6,D6,FALSE)

2. Calculate the probability of at most 6 successes out of 14 trials.

Select a cell (E7 in this case), copy or enter the formula below and press Enter to get the result.

=BINOM.DIST(B7,C7,D7,TRUE)

Related Functions

Excel BINOMDIST function
The BINOMDIST function returns the individual term binominal distribution probability.


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