bernoulli trials: meaning, definition, pronunciation and examples
Low (C2 / Specialized)Technical / Academic (primarily mathematics, statistics, engineering, physics)
Quick answer
What does “bernoulli trials” mean?
In probability and statistics, a sequence of independent experiments or random events, each of which has exactly two possible outcomes (often termed 'success' and 'failure') with constant probability for each trial.
Audio
Pronunciation
Definition
Meaning and Definition
In probability and statistics, a sequence of independent experiments or random events, each of which has exactly two possible outcomes (often termed 'success' and 'failure') with constant probability for each trial.
A fundamental statistical model forming the basis for the binomial distribution, used to model processes where outcomes are binary, independent, and identically distributed. It is also conceptually applied metaphorically to any situation with repeated, independent yes/no choices or outcomes.
Dialectal Variation
British vs American Usage
Differences
No significant differences in meaning or usage. Spelling conventions follow standard BrE/AmE rules in surrounding text (e.g., BrE 'modelling', AmE 'modeling').
Connotations
Identical technical connotations in both dialects.
Frequency
Equal frequency in relevant academic/technical fields in both regions.
Grammar
How to Use “bernoulli trials” in a Sentence
The process can be modelled [as] a sequence of Bernoulli trials.We performed [NUMBER] Bernoulli trials.The assumption [of] independent Bernoulli trials is crucial.Vocabulary
Collocations
Examples
Examples of “bernoulli trials” in a Sentence
adjective
British English
- The Bernoulli trial framework is inapplicable here.
- We need a Bernoulli-trial model.
American English
- The Bernoulli trial framework is inapplicable here.
- We need a Bernoulli-trial model.
Usage
Meaning in Context
Business
Rare. Potentially used in quantitative risk analysis or A/B testing frameworks where user choices are binary and independent.
Academic
Core concept in probability theory, statistics, and related STEM fields. Frequently used in textbooks and research papers.
Everyday
Virtually never used. The concept might be described in lay terms as 'a series of coin flips'.
Technical
The primary domain of use. Found in statistical software documentation, engineering reliability testing, and algorithm design (e.g., probabilistic algorithms).
Vocabulary
Synonyms of “bernoulli trials”
Strong
Neutral
Weak
Vocabulary
Antonyms of “bernoulli trials”
Watch out
Common Mistakes When Using “bernoulli trials”
- Using it to describe dependent events (e.g., drawing cards without replacement).
- Assuming the probability can change between trials and still calling them Bernoulli trials.
- Pronouncing 'Bernoulli' as 'ber-NOO-lee' instead of 'ber-NOO-lee' (stress on second syllable).
- Misspelling as 'Bernouli' or 'Bernolli'.
FAQ
Frequently Asked Questions
A single coin flip is a *Bernoulli trial*. A sequence of coin flips is a sequence of *Bernoulli trials*, which generates a binomial distribution if you count the number of heads.
Bernoulli trials describe the *process*: the sequence of independent, identical binary experiments. The Binomial distribution describes the *outcome*: the probability distribution of the total number of successes in a fixed number of such trials.
Yes, statistically. 'Success' is simply the label for the outcome of interest (e.g., a machine failing, a patient testing positive). The probability 'p' is the probability of that named event occurring, regardless of its desirability.
They are the simplest non-trivial probability model and form the building block for more complex models like the Binomial, Geometric, and Negative Binomial distributions. They are fundamental to statistical inference, hypothesis testing, and modelling binary data.
In probability and statistics, a sequence of independent experiments or random events, each of which has exactly two possible outcomes (often termed 'success' and 'failure') with constant probability for each trial.
Bernoulli trials is usually technical / academic (primarily mathematics, statistics, engineering, physics) in register.
Bernoulli trials: in British English it is pronounced /bɜːˈnuːli ˌtraɪəlz/, and in American English it is pronounced /bɝˈnuːli ˌtraɪəlz/. Tap the audio buttons above to hear it.
Phrases
Idioms & Phrases
- “It's not a Bernoulli trial. (Informal metaphor for a situation that isn't simple or independent)”
Learning
Memory Aids
Mnemonic
Think of Jacob Bernoulli flipping the same coin repeatedly. **Bern**-oulli **Tri**als = **Bern Tri** (Be Earnest & Try): Be earnest in ensuring each trial is Independent, and Try to keep the probability constant.
Conceptual Metaphor
COIN TOSSES / LIGHT SWITCHES: The quintessential metaphor is a sequence of fair or biased coin flips. Also like a row of identical, independent on/off switches.
Practice
Quiz
Which of the following scenarios best exemplifies a series of Bernoulli trials?