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.


Probability of success on a single trial [p]:*
Number of trials [n]:*
Number of successes [s]:*

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)! ] } * Ps * (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 | 0 comments

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