1. What is Hypergeometric Distribution?

The hypergeometric distribution describes the probability of k successes in n draws without replacement from a finite population of size N containing exactly K successes. It's used when sampling without replacement from a finite population.

2. How Does the Calculator Work?

The calculator uses the hypergeometric probability formula:

Where:

• \( N \) — Population size
• \( K \) — Number of successes in population
• \( n \) — Sample size
• \( k \) — Number of observed successes in sample
• \( \binom{a}{b} \) — Combination of a choose b

Explanation: The formula calculates the probability of getting exactly k successes in n draws from a population of size N containing K successes.

3. When to Use Hypergeometric Distribution

Details: Use this distribution when sampling without replacement from a finite population. Common applications include quality control, lottery probabilities, and biological sampling.

4. Using the Calculator

Tips: Enter all positive integer values where:

• K ≤ N
• n ≤ N
• k ≤ min(K, n)

5. Frequently Asked Questions (FAQ)

Q1: How is this different from binomial distribution?
A: Binomial distribution assumes sampling with replacement, while hypergeometric assumes sampling without replacement from a finite population.

Q2: What if my sample size is large?
A: For large N relative to n, hypergeometric approaches binomial distribution.

Q3: Can I use this for continuous data?
A: No, hypergeometric distribution is for discrete counts only.

Q4: What are common applications?
A: Quality control (defective items), ecological studies (species counts), and card game probabilities.

Q5: How accurate is the calculation?
A: The calculation is mathematically exact, though numerical precision may be limited for very large numbers.