BINOMDIST

Description Computes the binomial distribution, which is used to determine probabilities on repeated tests where each test is independent of every other test (that is, the probability is the same for each test).

Syntax BINOMDIST (successes, trials, probability, cumulative)

Argument Description

successes An integer describing the number of successes in the test. It must be a number larger than or equal to 0 and smaller than trials.

trials An integer describing the total number of attempts in the test. It must be a number larger than successes and smaller than the largest positive integer the machine can handle.

probability A value between 0 and 1 that represents the chance of success on an individual attempt. For example, the probability of heads in a coin toss is considered to be 0.5; the probability of getting "snake eyes" (two ones) when throwing a pair of dice is 1/36 or 0.02778.

cumulative A boolean value indicating the type of calculation you want. Enter FALSE to calculate the possibility of the success case (for example, getting exactly 3 heads in 4 coin tosses). Enter TRUE to calculate the sum of all cases from 0 to the success case (for example, for the probability of getting 0 or 1 or 2 or 3 heads in 4 coin tosses).

Argument	Description
successes	An integer describing the number of successes in the test. It must be a number larger than or equal to 0 and smaller than trials.
trials	An integer describing the total number of attempts in the test. It must be a number larger than successes and smaller than the largest positive integer the machine can handle.
probability	A value between 0 and 1 that represents the chance of success on an individual attempt. For example, the probability of heads in a coin toss is considered to be 0.5; the probability of getting "snake eyes" (two ones) when throwing a pair of dice is 1/36 or 0.02778.
cumulative	A boolean value indicating the type of calculation you want. Enter FALSE to calculate the possibility of the success case (for example, getting exactly 3 heads in 4 coin tosses). Enter TRUE to calculate the sum of all cases from 0 to the success case (for example, for the probability of getting 0 or 1 or 2 or 3 heads in 4 coin tosses).

Remarks Coin tosses or die rolls are examples of uses for BINOMDIST. For cases of sampling without replacement, use HYPGEOMDIST.

BINOMDIST is similar to NEGBINOMDIST, only in BINOMDIST the number of successes is variable and the number of trials is fixed, while in NEGBINOMDIST the number of successes is fixed and the number of trials is variable.

Equations When cumulative is FALSE:

When cumulative is TRUE:

Examples The following examples return the probabilities of getting a 6 on a die roll.

This function calculates the possibility of getting a 6 exactly once in 6 trials. It returns 0.401878:

BINOMDIST(1,6,0.166666667,FALSE)

This function calculates the possibility of getting a 6 zero or 1 time in 6 trials. It returns 0.736776:

BINOMDIST(1,6,0.166666667,TRUE)