binomial distribution: meaning, definition, pronunciation and examples

C2
UK/baɪˌnəʊ.mi.əl ˌdɪs.trɪˈbjuː.ʃən/US/baɪˌnoʊ.mi.əl ˌdɪs.trɪˈbjuː.ʃən/

Academic, Technical

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Quick answer

What does “binomial distribution” mean?

A discrete probability distribution that describes the number of successes in a fixed number of independent trials, each with the same probability of success.

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Pronunciation

Definition

Meaning and Definition

A discrete probability distribution that describes the number of successes in a fixed number of independent trials, each with the same probability of success.

In statistics, it models the probability of observing a specific number of successes (e.g., heads, 'yes' votes) out of a given number of independent binary (yes/no, success/failure) experiments.

Dialectal Variation

British vs American Usage

Differences

Spelling: 'distribution' is consistent. Concept and terminology are identical across varieties.

Connotations

None beyond its technical meaning.

Frequency

Used with equal frequency in UK and US academic/technical contexts.

Grammar

How to Use “binomial distribution” in a Sentence

[verb] a binomial distribution (calculate, use, follow)The binomial distribution with parameters n and pdistributed according to a binomial distribution

Vocabulary

Collocations

strong
calculate afollows aapproximate amodel with aparameter of the
medium
apply thestandardunderlyingassume a
weak
simpleexacttheoretical

Usage

Meaning in Context

Business

Rare, except in highly quantitative fields like risk analysis or quality control (e.g., 'We used a binomial distribution to model defect rates.').

Academic

Core term in statistics, probability theory, data science, and research methodology courses and papers.

Everyday

Virtually never used in everyday conversation.

Technical

Fundamental concept in statistics, engineering, bioinformatics, and any field involving binary outcome analysis.

Vocabulary

Synonyms of “binomial distribution”

Neutral

Bernoulli distribution (for n=1)

Weak

discrete distribution (broader hypernym)

Vocabulary

Antonyms of “binomial distribution”

continuous distributionnormal distribution (as a contrasting model for continuous data)

Watch out

Common Mistakes When Using “binomial distribution”

  • Using it for non-discrete or non-binary data.
  • Confusing it with the normal distribution.
  • Misspelling 'binomial' as 'binominal'.
  • Forgetting the assumptions: fixed n, independence, constant p.

FAQ

Frequently Asked Questions

Two parameters: n (number of trials) and p (probability of success in each trial).

No, it is strictly for discrete counts of successes.

A Bernoulli distribution is a special case of the binomial distribution where the number of trials n=1.

When trials are not independent, the number of trials is not fixed, or the probability of success changes between trials.

A discrete probability distribution that describes the number of successes in a fixed number of independent trials, each with the same probability of success.

Binomial distribution is usually academic, technical in register.

Binomial distribution: in British English it is pronounced /baɪˌnəʊ.mi.əl ˌdɪs.trɪˈbjuː.ʃən/, and in American English it is pronounced /baɪˌnoʊ.mi.əl ˌdɪs.trɪˈbjuː.ʃən/. Tap the audio buttons above to hear it.

Learning

Memory Aids

Mnemonic

BI-nomial has TWO (bi-) possible outcomes in each trial: success or failure. It counts successes in a fixed number of trials.

Conceptual Metaphor

A counting machine for 'wins' in a series of identical coin flips (where the coin can be biased).

Practice

Quiz

Fill in the gap
If you conduct 20 independent trials with a success probability of 0.3, the number of successes follows a .
Multiple Choice

Which of the following is a necessary condition for a binomial distribution?