What is Probability in Mathematics?
In Mathematics, Probability theory is the study of chances. In real life, we predict chances depending on the situation. But Probability theory is bringing a mathematical foundation for the concept of Probability. For example, if a box contain 10 balls which include 7 black balls and 3 red balls and randomly chosen one ball. Then the Probability of getting red ball is 3/10 and Probability of getting black ball is 7/10. When coming to statistics, Probability is like the back bone of statistics. It has a wide application in decision making, data science, business trend studies, etc.
What is Hypergeometric Distribution?
The Hypergeometric Distribution is a discrete probability distribution that describes the number of successes in a fixed number of Bernoulli trials (i.e. trials with only two possible outcomes: success or failure) without replacement. The probability mass function (PMF) of the hypergeometric distribution is given by: P(X = x) = (C(K,x) * C(N-K,n-x)) / C(N,n) The Hypergeometric Distribution is used to model the probability of observing a certain number of "successes" in a fixed number of draws from a finite population, where the probability of success changes on each draw. It is used in many fields such as genetics, quality control, and sampling inspection, in which the sample is drawn without replacement.
How to Calculate Hypergeometric Distribution?
Hypergeometric Distribution calculator uses Hypergeometric Probability Distribution Function = (C(Number of Items in Sample,Number of Successes in Sample)*C(Number of Items in Population-Number of Items in Sample,Number of Successes in Population-Number of Successes in Sample))/(C(Number of Items in Population,Number of Successes in Population)) to calculate the Hypergeometric Probability Distribution Function, The Hypergeometric Distribution formula is defined as the probability of obtaining a specific number of successes in a sample drawn without replacement from a finite population, where each element is classified into one of two categories (success or failure). Hypergeometric Probability Distribution Function is denoted by P_{Hypergeometric} symbol.
How to calculate Hypergeometric Distribution using this online calculator? To use this online calculator for Hypergeometric Distribution, enter Number of Items in Sample (m_{Sample}), Number of Successes in Sample (x_{Sample}), Number of Items in Population (N_{Population}) & Number of Successes in Population (n_{Population}) and hit the calculate button. Here is how the Hypergeometric Distribution calculation can be explained with given input values -> 0.044177 = (C(5,3)*C(50-5,10-3))/(C(50,10)).