Hypergeometric Distribution Calculator
This calculator is designed for statisticians and data analysts to compute probabilities using the hypergeometric distribution. It helps solve problems where you have a population with two types of objects and you are interested in the probability of drawing a specific number of objects of one type.
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Data Source and Methodology
All calculations are based strictly on the formulas and data provided by StatTrek. All computations adhere to these statistical principles.
The Formula Explained
\[ P(X = k) = \frac{{\binom{K}{k} \cdot \binom{N-K}{n-k}}}{{\binom{N}{n}}} \]
Glossary of Terms
- Population Size (N): Total number of items in the population.
- Number of Successes in Population (K): Number of items classified as "success" in the population.
- Sample Size (n): Number of items drawn from the population.
- Number of Successes in Sample (k): Number of items classified as "success" in the sample.
How It Works: A Step-by-Step Example
Suppose a deck of 52 cards contains 4 aces. We draw 5 cards. What is the probability of drawing exactly 2 aces?
Using the formula: \[ P(X = 2) = \frac{{\binom{4}{2} \cdot \binom{48}{3}}}{{\binom{52}{5}}} \]
Frequently Asked Questions (FAQ)
What is the hypergeometric distribution?
The hypergeometric distribution describes the probability of k successes in n draws, without replacement, from a finite population of size N containing K successes.
How does it differ from the binomial distribution?
Unlike the binomial distribution, the hypergeometric distribution is used for sampling without replacement.
Is this calculator suitable for large populations?
Yes, but computational complexity increases with larger numbers.
Can I use this for quality control?
Yes, it's commonly used in quality control to determine the defect rate.
What happens if my inputs are not valid?
Ensure all inputs are positive integers and make logical sense in context.