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Binomial Distribution (B₍n,p₎) ○◂｜Definition｜1st｜20260604231540-00-⌔
Binomial distribution - Wikipedia
Binomial distribution
In probability theory and statistics, the binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a sequence of n independent experiments, each asking a yes–no question, and each with its own Boolean -valued outcome: success (with probability p) or failure (with probability q = 1 − p). A single success/failure experiment is also called a Bernoulli trial or Bernoulli experiment, and a sequence of outcomes is called a Bernoulli process. For a single trial, that is, when n = 1, the binomial distribution is a Bernoulli distribution. The binomial distribution is the basis for the binomial test of statistical significance.1
The binomial distribution is frequently used to model the number of successes in a sample of size n drawn with replacement from a population of size N. If the sampling is carried out without replacement, the draws are not independent and so the resulting distribution is a hypergeometric distribution, not a binomial one. However, for N much larger than n, the binomial distribution remains a good approximation, and is widely used.
Printed 2026-06-28.
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Link to original Footnotes
Westland, J. Christopher (2020). Audit Analytics: Data Science for the Accounting Profession. Chicago: Springer Publishing. p. 53. ISBN 978-3-030-49091-1. ↩
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