Binomial distribution

Returns either the binomial probability or the cumulative binomial probability of variables n and p. This function is used in cases in which:

• There is a fixed number of tests
• Each test can only result in either success or failure (binary)
• Tests are independent of all other tests
• The probability of success is constant, for example, to calculate the probability that two out of the next three babies will be male

Syntax

BinomialDistribution <Cumulative> (x, n, p)

Where:

x is the number of successes.

n is the number of tests.

p is the number indicating the probability of a success in each trial.

Cumulative is a logical value that determines the form of the function.

• If Cumulative=0, it computes the Cumulative Binomial probability.
• If Cumulative=1, it computes the Binomial probability.

Expression

For the binomial probability:

Where:

is Combine(n, x).

The cumulative binomial distribution is:

Usage Notes

If x or n is not an integer, it is truncated.

The following conditions are invalid:

• One of the arguments is nonnumeric.
• x > n
• x< 0
• p < 0 or p > 1