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Binomial Probability Distribution Calculator

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✖Total Number of Trials is the total number of repetition of a particular random experiment, under similar circumstances.ⓘ Total Number of Trials [n_{Total Trials}]			+10% -10%
✖Number of Successful Trials is the required number of successes of a particular event in multiple rounds of a random experiment that follows a binomial distribution.ⓘ Number of Successful Trials [r]			+10% -10%
✖Probability of Success in Binomial Distribution is the likelihood of winning an event.ⓘ Probability of Success in Binomial Distribution [p_BD]			+10% -10%
✖Probability of Failure is the likelihood of losing an event.ⓘ Probability of Failure [q]			+10% -10%

✖Binomial Probability is the fraction of the number of times of successful completion of a particular event in multiple rounds of a random experiment which follows binomial distribution.ⓘ Binomial Probability Distribution [P_Binomial]

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Binomial Probability Distribution Solution

STEP 0: Pre-Calculation Summary

Formula Used

Binomial Probability = (C(Total Number of Trials,Number of Successful Trials))*Probability of Success in Binomial Distribution^Number of Successful Trials*Probability of Failure^(Total Number of Trials-Number of Successful Trials)
P_Binomial = (C(n_{Total Trials},r))*p_BD^r*q^(n_{Total Trials}-r)
This formula uses 1 Functions, 5 Variables

Functions Used

C - In combinatorics, the binomial coefficient is a way to represent the number of ways to choose a subset of objects from a larger set. It is also known as the "n choose k" tool., C(n,k)

Variables Used

Binomial Probability - Binomial Probability is the fraction of the number of times of successful completion of a particular event in multiple rounds of a random experiment which follows binomial distribution.
Total Number of Trials - Total Number of Trials is the total number of repetition of a particular random experiment, under similar circumstances.
Number of Successful Trials - Number of Successful Trials is the required number of successes of a particular event in multiple rounds of a random experiment that follows a binomial distribution.
Probability of Success in Binomial Distribution - Probability of Success in Binomial Distribution is the likelihood of winning an event.
Probability of Failure - Probability of Failure is the likelihood of losing an event.

STEP 1: Convert Input(s) to Base Unit

Total Number of Trials: 20 --> No Conversion Required
Number of Successful Trials: 4 --> No Conversion Required
Probability of Success in Binomial Distribution: 0.6 --> No Conversion Required
Probability of Failure: 0.4 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

P_Binomial = (C(n_{Total Trials},r))*p_BD^r*q^(n_{Total Trials}-r) --> (C(20,4))*0.6^4*0.4^(20-4)

Evaluating ... ...

P_Binomial = 0.000269686150476595

STEP 3: Convert Result to Output's Unit

0.000269686150476595 --> No Conversion Required

FINAL ANSWER

0.000269686150476595 ≈ 0.00027 <-- Binomial Probability

(Calculation completed in 00.004 seconds)

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< Binomial Distribution Calculators

Standard Deviation of Binomial Distribution

LaTeX Go Standard Deviation in Normal Distribution = sqrt(Number of Trials*Probability of Success*Probability of Failure in Binomial Distribution)

Mean of Negative Binomial Distribution

LaTeX Go Mean in Normal Distribution = (Number of Success*Probability of Failure in Binomial Distribution)/Probability of Success

Variance of Binomial Distribution

LaTeX Go Variance of Data = Number of Trials*Probability of Success*Probability of Failure in Binomial Distribution

Mean of Binomial Distribution

LaTeX Go Mean in Normal Distribution = Number of Trials*Probability of Success

Binomial Probability Distribution Formula

LaTeX Go

What is Probability?

In Mathematics, Probability theory is the study of chances. In real life, we predict chances depending on the situation. But Probability theory is bringing a mathematical foundation for the concept of Probability. For example, if a box contain 10 balls which include 7 black balls and 3 red balls and randomly chosen one ball. Then the Probability of getting red ball is 3/10 and Probability of getting black ball is 7/10. When coming to statistics, Probability is like the back bone of statistics. It has a wide application in decision making, data science, business trend studies, etc.

How to Calculate Binomial Probability Distribution?

Binomial Probability Distribution calculator uses Binomial Probability = (C(Total Number of Trials,Number of Successful Trials))*Probability of Success in Binomial Distribution^Number of Successful Trials*Probability of Failure^(Total Number of Trials-Number of Successful Trials) to calculate the Binomial Probability, The Binomial Probability Distribution formula is defined as the likelihood of obtaining a specific number of successful trials in a fixed number of independent trials, where each trial can result in one of two outcomes (success or failure), and the probability of success in each trial remains constant. Binomial Probability is denoted by P_Binomial symbol.

How to calculate Binomial Probability Distribution using this online calculator? To use this online calculator for Binomial Probability Distribution, enter Total Number of Trials (n_{Total Trials}), Number of Successful Trials (r), Probability of Success in Binomial Distribution (p_BD) & Probability of Failure (q) and hit the calculate button. Here is how the Binomial Probability Distribution calculation can be explained with given input values -> 17.67415 = (C(20,4))*0.6^4*0.4^(20-4).

FAQ

What is Binomial Probability Distribution?

The Binomial Probability Distribution formula is defined as the likelihood of obtaining a specific number of successful trials in a fixed number of independent trials, where each trial can result in one of two outcomes (success or failure), and the probability of success in each trial remains constant and is represented as P_Binomial = (C(n_{Total Trials},r))*p_BD^r*q^(n_{Total Trials}-r) or Binomial Probability = (C(Total Number of Trials,Number of Successful Trials))*Probability of Success in Binomial Distribution^Number of Successful Trials*Probability of Failure^(Total Number of Trials-Number of Successful Trials). Total Number of Trials is the total number of repetition of a particular random experiment, under similar circumstances, Number of Successful Trials is the required number of successes of a particular event in multiple rounds of a random experiment that follows a binomial distribution, Probability of Success in Binomial Distribution is the likelihood of winning an event & Probability of Failure is the likelihood of losing an event.

How to calculate Binomial Probability Distribution?

The Binomial Probability Distribution formula is defined as the likelihood of obtaining a specific number of successful trials in a fixed number of independent trials, where each trial can result in one of two outcomes (success or failure), and the probability of success in each trial remains constant is calculated using Binomial Probability = (C(Total Number of Trials,Number of Successful Trials))*Probability of Success in Binomial Distribution^Number of Successful Trials*Probability of Failure^(Total Number of Trials-Number of Successful Trials). To calculate Binomial Probability Distribution, you need Total Number of Trials (n_{Total Trials}), Number of Successful Trials (r), Probability of Success in Binomial Distribution (p_BD) & Probability of Failure (q). With our tool, you need to enter the respective value for Total Number of Trials, Number of Successful Trials, Probability of Success in Binomial Distribution & Probability of Failure 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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