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## Credits

Softusvista Office (Pune), India
Team Softusvista has created this Calculator and 500+ more calculators!
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## Binomial Probability Solution

STEP 0: Pre-Calculation Summary
Formula Used
binomial_probability = Combination Probability (nCr)*((Probability of Success)^r Items)*((Probability of Failure)^(n Set-r Items))
Bp = nCr*((p)^r)*((1-p)^(n-r))
This formula uses 5 Variables
Variables Used
Combination Probability (nCr)- Combination Probability is the number of ways of selecting r items from a set of n.
Probability of Success- Probability of Success is the ratio of success cases over all outcomes.
r Items- r Items are the total items that can be selected from the available set.
Probability of Failure- The Probability of Failure is defined as the probability of exceeding a limit state within a defined reference time period.
n Set- n Set is the total number of the available sets from which items will be selected.
STEP 1: Convert Input(s) to Base Unit
Combination Probability (nCr): 120 --> No Conversion Required
Probability of Success: 0.75 --> No Conversion Required
r Items: 9 --> No Conversion Required
Probability of Failure: 0.25 --> No Conversion Required
n Set: 20 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Bp = nCr*((p)^r)*((1-p)^(n-r)) --> 120*((0.75)^9)*((0.25)^(20-9))
Evaluating ... ...
Bp = 2.14819010579959E-06
STEP 3: Convert Result to Output's Unit
2.14819010579959E-06 --> No Conversion Required
2.14819010579959E-06 <-- Binomial Probability
(Calculation completed in 00.047 seconds)
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## < 11 Other formulas that you can solve using the same Inputs

Standard deviation of binomial distribution
standard_deviation = sqrt((Number of trials)*(Probability of Success)*(1-Probability of Success)) Go
Standard deviation of negative binomial distribution
standard_deviation = sqrt((Number of success*Probability of Failure)/(Probability of Success)) Go
Combination Probability
combination_probability = (n Set)!/((r Items)!*(n Set-r Items)!) Go
Variance of negative binomial distribution.
variance_distribution = (Number of success*Probability of Failure)/(Probability of Success^2) Go
Mean of negative binomial distribution
mean_distribution = (Number of success*Probability of Failure)/Probability of Success Go
variance of binomial distribution
variance = Number of trials*Probability of Success*(1-Probability of Success) Go
Standard deviation of geometric distribution
standard_deviation = sqrt(Probability of Failure/(Probability of Success^2)) Go
Variance population proportion
variance = (Probability of Success*Probability of Failure)/Number of trials Go
Variance of geometric distribution.
variance_distribution = Probability of Failure/(Probability of Success^2) Go
Mean of geometric distribution
mean_distribution = Probability of Failure/Probability of Success Go
mean of binomial distribution
mean_distribution = Probability of Success*Number of trials Go

### Binomial Probability Formula

binomial_probability = Combination Probability (nCr)*((Probability of Success)^r Items)*((Probability of Failure)^(n Set-r Items))
Bp = nCr*((p)^r)*((1-p)^(n-r))

## What is Binomial Probability?

Binomial Probability is the probability that an n-trial binomial experiment results in exactly x successes, when the probability of success on an individual trial is P. In other words, binomial probability refers to the probability of exactly x successes on n repeated trials in an experiment which has two possible outcomes (commonly called a binomial experiment) was found by a swiss mathematician Jakob Bernoulli, in a proof published posthumously in 1713.

## How to Calculate Binomial Probability?

Binomial Probability calculator uses binomial_probability = Combination Probability (nCr)*((Probability of Success)^r Items)*((Probability of Failure)^(n Set-r Items)) to calculate the Binomial Probability, Binomial probability refers to the probability that a binomial experiment results in exactly x successes. Binomial Probability and is denoted by Bp symbol.

How to calculate Binomial Probability using this online calculator? To use this online calculator for Binomial Probability, enter Combination Probability (nCr) (nCr), Probability of Success (p), r Items (r), Probability of Failure (1-p) and n Set (n) and hit the calculate button. Here is how the Binomial Probability calculation can be explained with given input values -> 2.148E-6 = 120*((0.75)^9)*((0.25)^(20-9)).

### FAQ

What is Binomial Probability?
Binomial probability refers to the probability that a binomial experiment results in exactly x successes and is represented as Bp = nCr*((p)^r)*((1-p)^(n-r)) or binomial_probability = Combination Probability (nCr)*((Probability of Success)^r Items)*((Probability of Failure)^(n Set-r Items)). Combination Probability is the number of ways of selecting r items from a set of n, Probability of Success is the ratio of success cases over all outcomes, r Items are the total items that can be selected from the available set, The Probability of Failure is defined as the probability of exceeding a limit state within a defined reference time period and n Set is the total number of the available sets from which items will be selected.
How to calculate Binomial Probability?
Binomial probability refers to the probability that a binomial experiment results in exactly x successes is calculated using binomial_probability = Combination Probability (nCr)*((Probability of Success)^r Items)*((Probability of Failure)^(n Set-r Items)). To calculate Binomial Probability, you need Combination Probability (nCr) (nCr), Probability of Success (p), r Items (r), Probability of Failure (1-p) and n Set (n). With our tool, you need to enter the respective value for Combination Probability (nCr), Probability of Success, r Items, Probability of Failure and n Set and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
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