sample space
C2Technical/Academic
Definition
Meaning
In probability theory, the set of all possible outcomes of a random experiment.
The complete collection of distinct outcomes that could occur in a given probabilistic scenario; the universal set for a probability model.
Linguistics
Semantic Notes
Always used as a compound noun; primarily appears in mathematics, statistics, data science, and formal reasoning contexts. Not used in everyday conversation.
Dialectal Variation
British vs American Usage
Differences
No significant differences in meaning or usage between British and American English. Both use the term identically in technical contexts.
Connotations
Purely technical term with no cultural or regional connotations.
Frequency
Equally frequent in academic and technical writing in both varieties.
Vocabulary
Collocations
Grammar
Valency Patterns
The sample space of [experiment] is [set].We must first determine the sample space.Each outcome in the sample space...Let S denote the sample space.Vocabulary
Synonyms
Strong
Neutral
Weak
Vocabulary
Antonyms
Phrases
Idioms & Phrases
- “None”
Usage
Context Usage
Business
Rare, except in data analysis or risk assessment reports.
Academic
Common in mathematics, statistics, engineering, and physics textbooks and papers.
Everyday
Virtually never used.
Technical
Core term in probability theory, statistics, machine learning, and quantitative research.
Examples
By Part of Speech
verb
British English
- Not applicable as a verb.
American English
- Not applicable as a verb.
adverb
British English
- Not applicable as an adverb.
American English
- Not applicable as an adverb.
adjective
British English
- Not applicable as an adjective.
American English
- Not applicable as an adjective.
Examples
By CEFR Level
- Not typically taught at this level.
- Not typically taught at this level.
- When you roll a die, the sample space is {1, 2, 3, 4, 5, 6}.
- The sample space for a coin toss is {heads, tails}.
- Before calculating any probabilities, one must rigorously define the sample space of the random process.
- The researcher enumerated all combinations to construct the sample space for the complex experiment.
Learning
Memory Aids
Mnemonic
Think of a 'space' containing every possible 'sample' result from an experiment, like a bag holding all the different tickets you could draw.
Conceptual Metaphor
A CONTAINER holding all POSSIBILITIES.
Watch out
Common Pitfalls
Translation Traps (for Russian speakers)
- Avoid translating 'sample' as 'образец' (specimen) here. It means 'выборка' in the sense of a set of outcomes.
- Do not confuse with 'выборочное пространство' – a direct calque that is not standard. Use 'пространство элементарных событий' or 'пространство исходов'.
Common Mistakes
- Using 'sample space' to refer to a physical space where samples are taken (e.g., in a lab).
- Confusing 'sample space' (all outcomes) with 'event' (a subset of outcomes).
- Treating it as a countable noun (e.g., 'a sample space' is fine, but 'two sample spaces' is only correct when comparing two different experiments).
Practice
Quiz
Which of the following best describes a 'sample space'?
FAQ
Frequently Asked Questions
No. A 'population' is the entire group you want to study, while a 'sample space' is the set of all possible outcomes of a random experiment, often used in theoretical probability.
Yes. For example, the sample space for 'the time until a radioactive atom decays' is the infinite set of all positive real numbers.
Yes, it is a fixed compound noun. The stress is typically on the first word: 'SAMPLE space'.
You might see it in fields that use formal probability models, such as quantum physics, algorithmic game theory, actuarial science, or advanced machine learning research.