binomial distribution: meaning, definition, pronunciation and examples
C2Academic, Technical
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.
Audio
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 distributionVocabulary
Collocations
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
Weak
Vocabulary
Antonyms of “binomial distribution”
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
Which of the following is a necessary condition for a binomial distribution?