# BINOM.DIST

Formulas / BINOM.DIST
The BINOM.DIST formula calculates the binomial probability or the cumulative binomial distribution for a given number of successes, trials, and probability of success on each trial.
`BINOM.DIST(number_s, trials, probability_s, cumulative)`
• number_s - The number of successes in trials.
• trials - The number of independent trials.
• probability_s - The probability of success on each trial.
• cumulative - A logical value that determines the form of the function:
• TRUE: Returns the cumulative distribution function.
• FALSE: Returns the probability mass function.

## Examples

• `=BINOM.DIST(3, 10, 0.5, FALSE)`

This formula calculates the probability mass function of getting exactly 3 successes in 10 independent trials, each with a 50% probability of success (e.g., getting 3 heads in 10 coin flips). The result is the probability of this specific outcome.

• `=BINOM.DIST(3, 10, 0.5, TRUE)`

This formula calculates the cumulative distribution function of getting 3 or fewer successes in 10 independent trials, each with a 50% probability of success (e.g., getting 3 or fewer heads in 10 coin flips). The result is the cumulative probability of getting 0, 1, 2, or 3 successes.

## Summary

BINOM.DIST is a formula used to calculate the probability of a certain number of successes in a fixed number of trials with a specified probability of success.

• The BINOM.DIST function is a statistical function that calculates the binomial probability or the cumulative binomial distribution for a given number of successes ("number_s"), trials ("trials"), and probability of success on each trial ("probability_s").
• The "cumulative" argument is a logical value that specifies the form of the function: FALSE returns the probability mass function (probability of exactly "number_s" successes), while TRUE returns the cumulative distribution function (cumulative probability of "number_s" or fewer successes).
• BINOM.DIST requires "number_s" and "trials" to be whole numbers (integers) and "probability_s" to be within the range [0, 1]; otherwise, the function returns a #NUM! error. Fractional values for "number_s" or "trials" are not valid.

What does the BINOM.DIST function do?
The BINOM.DIST function calculates the binomial probability or the cumulative binomial distribution for a given set of parameters. It models the number of successes in a fixed number of trials, each with the same probability of success.
What are the arguments of the BINOM.DIST function?
The BINOM.DIST function has four arguments: "number_s" (the number of successes in trials), "trials" (the number of independent trials), "probability_s" (the probability of success on each trial), and "cumulative" (a logical value that specifies whether to return the probability mass function (FALSE) or the cumulative distribution function (TRUE)).
What is the difference between the probability mass function and the cumulative distribution function in BINOM.DIST?
The probability mass function (cumulative = FALSE) calculates the probability of getting exactly "number_s" successes in "trials" independent trials. The cumulative distribution function (cumulative = TRUE) calculates the cumulative probability of getting "number_s" or fewer successes in "trials" independent trials.
What happens if the arguments provided to BINOM.DIST are not valid?
If the arguments provided to BINOM.DIST are not valid (e.g., negative values for "number_s" or "trials," or a probability outside the range [0, 1]), the function returns a #NUM! error.
Can BINOM.DIST handle fractional values for the number of successes or trials?
No, BINOM.DIST requires "number_s" and "trials" to be whole numbers (integers). Fractional values for these arguments will result in a #NUM! error.

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