What are the limitations of the Binomial Distribution?

The Binomial Distribution assumes binary outcomes and independent trials, which may not always be applicable.

Binomial Distribution Calculator

Q: How do I use this calculator?

Enter the number of trials, probability of success, and number of successes to calculate the probability.

This calculator is designed for statisticians and data analysts to compute the probability of obtaining a given number of successes in a fixed number of trials with a constant probability of success.

Calculator

Results

Probability: -

Data Source and Methodology

All calculations are based strictly on the formulas and data provided by authoritative statistical sources.

The Formula Explained

The probability of getting exactly k successes in n trials is given by:

\( P(X = k) = \binom{n}{k} p^k (1-p)^{n-k} \)

Glossary of Variables

n: Number of trials.
p: Probability of success on an individual trial.
k: Number of successes.
\( \binom{n}{k} \): Binomial coefficient, representing the number of ways to choose k successes from n trials.

How It Works: A Step-by-Step Example

Suppose you flip a biased coin 10 times, where the probability of heads (success) is 0.5. What is the probability of getting exactly 5 heads?

Using the formula: \( P(X = 5) = \binom{10}{5} (0.5)^5 (1-0.5)^{10-5} \). Calculate each component to find the probability.

Frequently Asked Questions (FAQ)

What is the Binomial Distribution?

The Binomial Distribution represents the number of successes in a sequence of n independent experiments, each asking a yes/no question, and each with its own boolean-valued outcome.

How do I use this calculator?

Enter the number of trials, the probability of success, and the number of successes, then click 'Calculate' to see the probability.

What is the difference between Binomial and Normal distribution?

The Binomial Distribution is discrete, while the Normal Distribution is continuous. They are related through the Central Limit Theorem.

Can the probability be greater than 1?

No, probabilities range from 0 to 1.

What applications use the Binomial Distribution?

Common applications include quality control, finance, and health sciences where binary outcomes are analyzed.

Tool developed by Ugo Candido. Content reviewed by the Expert Team.
Last reviewed for accuracy on: October 1, 2023.

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