# Documentation/Calc Functions/B

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B

## Category:

Statistical Analysis

## Summary:

Returns the probability of a trial result using the binomial distribution.

## Syntax:

B(Trials; SP; T1 [; T2])

## Returns:

Returns a real number which is the probability of a trial and hence it is between 0(inclusive) and 1(inclusive).

## Arguments:

Trials is the number of independent trials.

SP is the probability of success on each trial.

T1 defines the lower limit for the number of trials.

T2 defines the upper limit for the number of trials.

• T1 and T2 lies between 0 and the independent number of trials for the function,i.e. [0,Trials].
• If Trials are a non-integer value, then the function truncates it to an integer.
• If Trials, T1 or T2 are less than zero, then the function returns an error value.
• If T1 is greater than T2, then the function returns an error value.
• If T2 greater than (Trials + 1), then the function returns an error value.
• If SP is greater than 1 or less than 0, then the function returns an error value.

## Additional details:

For more details on Binomial distribution, visit Wikipedia.

## Examples:

Formula Description Returns
=B(10;1/6;2) The function calculates the probability that a 6 will come up exactly twice in 10 throws of a single dice, assuming that the probability of a 6 (or any other number) coming up on a single throw is 1/6. 0.290710049201722
=B(10;1/6;3) The function calculates the probability that a 6 will come up exactly thrice in 10 throws of a single dice, assuming that the probability of a 6 (or any other number) coming up on a single throw is 1/6. 0.155045359574252
=B(10;1/6;2;3) The function calculates the sum of the probability that a 6 will come up exactly 2 times and 3 times, separately, in 10 throws of a single dice, assuming that the probability of a 6 (or any other number) coming up on a single throw is 1/6. 0.445755408775974
=B(10;1/6;2;10) The function calculates the sum of the probability that a 6 will come up exactly 2 times, 3 times, 4 times,...and 10 times, separately, in 10 throws of a single dice, assuming that the probability of a 6 (or any other number) coming up on a single throw is 1/6. 0.515483251330463
=B(10;1/6;2;11) There is no case possible when 11 times 6 appears for 10 throws hence the function returns an error value. Err:502

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