Binomial Distribution Calculator
Calculate binomial probabilities, mean, variance, and visualize the distribution curve.
Input Parameters
Value between 0 and 1
Probability P(X = x)
Probability Distribution Graph
Calculation Steps
Formula: P(X=x) = nCx * p^x * q^(n-x)
Where:
- n (trials) = 0
- x (successes) = 0
- p (probability) = 0
- q (1-p) = 0
Calculation for P(X=x):
= C * p^x * q^(n-x)
= 0
Enter parameters on the left to calculate binomial distribution.
About Binomial Distribution
The Binomial Distribution is a fundamental probability distribution that summarizes the likelihood that a value will take one of two independent values under a given set of parameters or assumptions. It is widely used in statistics to model the number of successes in a sample of size n drawn with replacement from a population of size N.
The Binomial Formula
The probability of getting exactly x successes in n independent Bernoulli trials is given by the probability mass function:
Where:
- n: Total number of trials
- x: Number of successes
- p: Probability of success on an individual trial
- nCx: The binomial coefficient (n choose x)
Frequently Asked Questions
How to calculate binomial distribution?
To calculate binomial distribution, you need three values: the number of trials (n), the probability of success in a single trial (p), and the number of successes you want to calculate the probability for (x). Plug these into the formula P(x) = (n! / (x!(n-x)!)) * p^x * (1-p)^(n-x).
What are the conditions for a binomial experiment?
A binomial experiment must satisfy four conditions: 1) Fixed number of trials, 2) Each trial is independent, 3) Only two outcomes (success or failure), and 4) Probability of success remains constant for each trial.
How to use this binomial probability distribution calculator?
Simply enter the number of trials (n), probability of success (p), and the specific number of successes (x). Select whether you want the exact probability, less than, or greater than, and click "Calculate". The tool will show the result, statistics, and a distribution graph.
What is the mean and variance of a binomial distribution?
The mean (expected value) is calculated as μ = n * p. The variance is calculated as σ² = n * p * (1 - p). The standard deviation is the square root of the variance.
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