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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
FINAL ANSWER
2.14819010579959E-06 <-- Binomial Probability
(Calculation completed in 00.000 seconds)
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6 Probability Calculators

Binomial Probability
binomial_probability = Combination Probability (nCr)*((Probability of Success)^R Items)*((Probability of Failure)^(N Set-R Items)) Go
Combination Probability
combination_probability = (N Set)!/((R Items)!*(N Set-R Items)!) Go
Empirical Probability
empirical_probability = Number of times event occurs/Total number of times experiment performed Go
Probability of event
probability_of_an_event = Number of Favorable Outcomes/Total Number of Possible Outcomes Go
Probability of failure
probability_of_failure = 1-Probability of Success Go
Probability of success
probability_of_success = 1-Probability of Failure 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) & 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 & 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) & 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 & N Set and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Binomial Probability?
In this formula, Binomial Probability uses Combination Probability (nCr), Probability of Success, R Items, Probability of Failure & N Set. We can use 6 other way(s) to calculate the same, which is/are as follows -
  • probability_of_an_event = Number of Favorable Outcomes/Total Number of Possible Outcomes
  • combination_probability = (N Set)!/((R Items)!*(N Set-R Items)!)
  • binomial_probability = Combination Probability (nCr)*((Probability of Success)^R Items)*((Probability of Failure)^(N Set-R Items))
  • empirical_probability = Number of times event occurs/Total number of times experiment performed
  • probability_of_failure = 1-Probability of Success
  • probability_of_success = 1-Probability of Failure
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