Multinomial Distribution Calculator

About this calculator

The multinomial distribution generalizes the binomial to situations with more than two possible outcomes. Given n independent trials where each falls into one of k categories with probabilities p₁, p₂, …, pₖ, the probability of observing exactly x₁, x₂, …, xₖ occurrences of each category is P = n! / (x₁!x₂!…xₖ!) × p₁^x₁ × p₂^x₂ × … × pₖ^xₖ.

Statisticians use it for goodness-of-fit and categorical data analysis, geneticists use it to model the joint probability of observing certain allele or genotype frequencies, quality control engineers use it when a defect can fall into several distinct categories, and survey and poll analysts use it to compute the probability of a specific split of responses across multiple answer choices.