This **binomial calculator** can help you calculate individual and cumulative binomial probabilities of an experiment considering the probability of success on a single trial, no. of trials and no. of successes. You can learn more below the form.

## How does this binomial calculator work?

This is a statistics tool designed to help you compute individual and cumulative binomial probabilities for an experiment having the following particularities:

■ The experiment requires *repeated trials* while each trial can have *one of the two potential outcomes*: either success or failure.

■ The probability associated with the occurrence of a particular outcome on any given trial *is constant*.

■ The trials *are independent*.

The algorithm behind this *binomial calculator* is based on the formulas provided below:

1) B(s=s given; n, p) = { n! / [ s! (n - s)! ] } * P^{s} * (1 - P)^{n – s}

2) B(s<s given; n, p) is the sum of probabilities obtained for all cases from (s=0) to (s given – 1).

3) B(s≤s given; n, p) is the sum of probabilities that results for all cases from (s=0) to (s given).

4) B(s>s given; n, p) = 1 - B(s≤s given; n, p)

5) B(s≥s given; n, p) = B(s=s given; n, p) + B(s>s given; n, p)

Where:

P = Probability of success on a single trial

n = Number of trials

s = Number of successes

## What is a binomial probability?

The binomial probability represents the probability of getting **an exact number of successes (s)** **in a given number of trials (n)** within an experiment.

## What is the cumulative binomial probability?

The cumulative binomial probability is obtained by **adding up the individual probabilities** of getting each number of successes within a specified range.

For instance the cumulative probability of extracting less than or equal 2 (s) white balls out of 6 (n) is equivalent to:

[the probability of extracting exactly 0 (s=0) white balls out of the 6] + [the probability of getting exactly 1 (s=1) ball in white out of 6] + [the probability of extracting exactly 2 (s=2) white balls]

27 Jul, 2015