A1 6 N 5 R 3 Calculator

This calculator helps you determine the probability of specific outcomes in statistical experiments using the A1 6 N 5 R 3 formula. Whether you're analyzing survey results, quality control data, or scientific experiments, this tool provides quick and accurate probability calculations.

What is A1 6 N 5 R 3?

The A1 6 N 5 R 3 formula is a statistical method used to calculate probabilities in scenarios where you have a sample size (n), population size (N), number of successes in the sample (x), and number of successes in the population (K). This is commonly used in quality control, survey sampling, and scientific research.

Key terms in the formula:

A1: The probability of success in the population
6: The number of trials or samples
N: The total population size
5: The number of successes in the sample
R: The number of successes in the population
3: The number of trials or samples with a specific outcome

How to Use the Calculator

Using the A1 6 N 5 R 3 calculator is straightforward:

Enter the probability of success in the population (A1)
Enter the number of trials or samples (6)
Enter the total population size (N)
Enter the number of successes in the sample (5)
Enter the number of successes in the population (R)
Enter the number of trials with a specific outcome (3)
Click "Calculate" to get the probability result

The calculator will display the calculated probability and provide an explanation of the result.

Formula Explanation

The A1 6 N 5 R 3 formula is based on the hypergeometric distribution, which is used when sampling is done without replacement. The formula is:

Formula

P = [C(R, x) × C(N-R, n-x)] / C(N, n)

Where:

P = Probability of the event
C = Combination function
R = Number of successes in the population
x = Number of successes in the sample
N = Total population size
n = Sample size

This formula calculates the probability of getting exactly x successes in a sample of size n from a population of size N that contains exactly R successes.

Example Calculation

Let's say you have a population of 100 items (N = 100), with 20 defective items (R = 20). You take a sample of 10 items (n = 10) and want to find the probability that exactly 2 items are defective (x = 2).

Using the formula:

Example Calculation

P = [C(20, 2) × C(80, 8)] / C(100, 10)

Where:

C(20, 2) = 190 (number of ways to choose 2 defective items from 20)
C(80, 8) = 17,885,700 (number of ways to choose 8 non-defective items from 80)
C(100, 10) = 173,103,094,564,400 (total number of ways to choose 10 items from 100)

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