Binomial Distribution Calculator

✖The Number of Trials is the number of times a certain probabilistic event is tried out multiple times.ⓘ Number of Trials [n_trials]			+10% -10%
✖The Probability of Success of Single Trial is the favorable possibility of the outcome of a certain individual event.ⓘ Probability of Success of Single Trial [p]			+10% -10%
✖Specific Outcomes within Trials are the number of times a certain outcome takes place within a given set of trials.ⓘ Specific Outcomes within Trials [x]			+10% -10%
✖The Probability of Failure of Single Trial is the favorable possibility of the outcome not happening for a certain individual event.ⓘ Probability of Failure of Single Trial [q]			+10% -10%

✖The binomial distribution can be thought of as simply the probability of a Success or Failure outcome in an experiment or survey that is repeated multiple times.ⓘ Binomial Distribution [P_binomial]

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Binomial Distribution Solution

STEP 0: Pre-Calculation Summary

Formula Used

Binomial Distribution = Number of Trials!*Probability of Success of Single Trial^Specific Outcomes within Trials*(Probability of Failure of Single Trial^(Number of Trials-Specific Outcomes within Trials))/(Specific Outcomes within Trials!*(Number of Trials-Specific Outcomes within Trials)!)
P_binomial = n_trials!*p^x*(q^(n_trials-x))/(x!*(n_trials-x)!)
This formula uses 5 Variables

Variables Used

Binomial Distribution - The binomial distribution can be thought of as simply the probability of a Success or Failure outcome in an experiment or survey that is repeated multiple times.
Number of Trials - The Number of Trials is the number of times a certain probabilistic event is tried out multiple times.
Probability of Success of Single Trial - The Probability of Success of Single Trial is the favorable possibility of the outcome of a certain individual event.
Specific Outcomes within Trials - Specific Outcomes within Trials are the number of times a certain outcome takes place within a given set of trials.
Probability of Failure of Single Trial - The Probability of Failure of Single Trial is the favorable possibility of the outcome not happening for a certain individual event.

STEP 1: Convert Input(s) to Base Unit

Number of Trials: 7 --> No Conversion Required
Probability of Success of Single Trial: 0.6 --> No Conversion Required
Specific Outcomes within Trials: 3 --> No Conversion Required
Probability of Failure of Single Trial: 0.4 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

P_binomial = n_trials!*p^x*(q^(n_trials-x))/(x!*(n_trials-x)!) --> 7!*0.6^3*(0.4^(7-3))/(3!*(7-3)!)

Evaluating ... ...

P_binomial = 0.193536

STEP 3: Convert Result to Output's Unit

0.193536 --> No Conversion Required

FINAL ANSWER

0.193536 <-- Binomial Distribution

(Calculation completed in 00.004 seconds)

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Created by Suman Ray Pramanik

Indian Institute of Technology (IIT), Kanpur

Suman Ray Pramanik has created this Calculator and 50+ more calculators!

Verified by Akshada Kulkarni

National Institute of Information Technology (NIIT), Neemrana

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< Industrial Parameters Calculators

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Binomial Distribution Formula

LaTeX Go

What is binomial distribution?

The binomial distribution can be thought of as simply the probability of a Success or Failure outcome in an experiment or survey that is repeated multiple times. The binomial distribution is a probability distribution that summarizes the likelihood that a value will take one of two independent values under a given set of parameters or assumptions.

How to Calculate Binomial Distribution?

Binomial Distribution calculator uses Binomial Distribution = Number of Trials!*Probability of Success of Single Trial^Specific Outcomes within Trials*(Probability of Failure of Single Trial^(Number of Trials-Specific Outcomes within Trials))/(Specific Outcomes within Trials!*(Number of Trials-Specific Outcomes within Trials)!) to calculate the Binomial Distribution, The binomial distribution can be thought of as simply the probability of a Success or Failure outcome in an experiment or survey that is repeated multiple times. Binomial Distribution is denoted by P_binomial symbol.

How to calculate Binomial Distribution using this online calculator? To use this online calculator for Binomial Distribution, enter Number of Trials (n_trials), Probability of Success of Single Trial (p), Specific Outcomes within Trials (x) & Probability of Failure of Single Trial (q) and hit the calculate button. Here is how the Binomial Distribution calculation can be explained with given input values -> 0.193536 = 7!*0.6^3*(0.4^(7-3))/(3!*(7-3)!).

FAQ

What is Binomial Distribution?

The binomial distribution can be thought of as simply the probability of a Success or Failure outcome in an experiment or survey that is repeated multiple times and is represented as P_binomial = n_trials!*p^x*(q^(n_trials-x))/(x!*(n_trials-x)!) or Binomial Distribution = Number of Trials!*Probability of Success of Single Trial^Specific Outcomes within Trials*(Probability of Failure of Single Trial^(Number of Trials-Specific Outcomes within Trials))/(Specific Outcomes within Trials!*(Number of Trials-Specific Outcomes within Trials)!). The Number of Trials is the number of times a certain probabilistic event is tried out multiple times, The Probability of Success of Single Trial is the favorable possibility of the outcome of a certain individual event, Specific Outcomes within Trials are the number of times a certain outcome takes place within a given set of trials & The Probability of Failure of Single Trial is the favorable possibility of the outcome not happening for a certain individual event.

How to calculate Binomial Distribution?

The binomial distribution can be thought of as simply the probability of a Success or Failure outcome in an experiment or survey that is repeated multiple times is calculated using Binomial Distribution = Number of Trials!*Probability of Success of Single Trial^Specific Outcomes within Trials*(Probability of Failure of Single Trial^(Number of Trials-Specific Outcomes within Trials))/(Specific Outcomes within Trials!*(Number of Trials-Specific Outcomes within Trials)!). To calculate Binomial Distribution, you need Number of Trials (n_trials), Probability of Success of Single Trial (p), Specific Outcomes within Trials (x) & Probability of Failure of Single Trial (q). With our tool, you need to enter the respective value for Number of Trials, Probability of Success of Single Trial, Specific Outcomes within Trials & Probability of Failure of Single Trial 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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