mathematical probability: meaning, definition, pronunciation and examples
C2/TechnicalFormal, Academic, Technical
Quick answer
What does “mathematical probability” mean?
A measure of the likelihood that a specific event will occur, expressed as a number between 0 and 1 (or 0% and 100%), calculated from a mathematical model of a random process. For example, the probability of flipping a fair coin and getting heads is 0.
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Pronunciation
Definition
Meaning and Definition
A measure of the likelihood that a specific event will occur, expressed as a number between 0 and 1 (or 0% and 100%), calculated from a mathematical model of a random process. For example, the probability of flipping a fair coin and getting heads is 0.5.
The rigorous branch of mathematics, known as probability theory, concerned with the analysis of random phenomena. It provides formal rules and frameworks (like axioms, distributions, and theorems) for quantifying uncertainty.
Dialectal Variation
British vs American Usage
Differences
No lexical differences. 'Maths' (UK) vs. 'math' (US) is used in the broader field name ('probability theory in maths/math'), but the compound term 'mathematical probability' is identical in both.
Connotations
Identical in both varieties.
Frequency
Slightly more frequent in American academic texts due to larger output in STEM fields, but the term itself has no regional preference.
Grammar
How to Use “mathematical probability” in a Sentence
The mathematical probability of [EVENT] is [NUMBER].We can calculate the mathematical probability that [CLAUSE].According to the principles of mathematical probability, ...Vocabulary
Collocations
Examples
Examples of “mathematical probability” in a Sentence
verb
British English
- The model allows us to probabilistically forecast outcomes.
- We can probabilistically assess the risk.
American English
- The system is designed to probabilistically determine the best path.
- They probabilistically modeled the network's failure points.
adverb
British English
- The event was considered probabilistically impossible.
- He argued probabilistically rather than definitively.
American English
- You can think about it probabilistically.
- The system behaves probabilistically, not deterministically.
adjective
British English
- A probabilistic framework underpins the analysis.
- He made a probabilistic assessment of the evidence.
American English
- The approach is fundamentally probabilistic.
- We need a probabilistic model for this scenario.
Usage
Meaning in Context
Business
Used in risk analysis and actuarial science to model financial risks.
Academic
Core concept in mathematics, statistics, physics, engineering, and quantitative social sciences.
Everyday
Rarely used precisely; people say 'chance' or 'likelihood' instead.
Technical
Fundamental term in probability theory, statistics, machine learning (e.g., probabilistic models), and quantum mechanics.
Vocabulary
Synonyms of “mathematical probability”
Strong
Neutral
Weak
Vocabulary
Antonyms of “mathematical probability”
Watch out
Common Mistakes When Using “mathematical probability”
- Using 'mathematical probability' to mean a rough guess or a subjective feeling. It must be derived from a mathematical model.
- Confusing it with 'statistical probability' (based on observed data).
- Misspelling 'probability' as 'probablity' or 'probabilty'.
FAQ
Frequently Asked Questions
Mathematical probability is derived from a theoretical model (e.g., a fair die has 6 sides). Statistical probability is estimated from observed data (e.g., it rained 15 out of 30 days last month).
No. By definition and axiom, a mathematical probability is always a real number between 0 and 1 inclusive (0 ≤ P ≤ 1).
No. Probability is a ratio of favorable outcomes to total possible outcomes (e.g., 1/4). Odds are a ratio of favorable to unfavorable outcomes (e.g., 1:3). They are mathematically related but expressed differently.
It provides the formal language to describe uncertainty, randomness, and risk. It is foundational for statistical inference, quantum physics, machine learning algorithms, and financial modeling, allowing precise predictions and decisions under uncertainty.
A measure of the likelihood that a specific event will occur, expressed as a number between 0 and 1 (or 0% and 100%), calculated from a mathematical model of a random process. For example, the probability of flipping a fair coin and getting heads is 0.
Mathematical probability is usually formal, academic, technical in register.
Mathematical probability: in British English it is pronounced /ˌmæθ.əˌmæt.ɪ.kəl ˌprɒb.əˈbɪl.ə.ti/, and in American English it is pronounced /ˌmæθ.əˌmæt̬.ɪ.kəl ˌprɑː.bəˈbɪl.ə.t̬i/. Tap the audio buttons above to hear it.
Phrases
Idioms & Phrases
- “The laws of probability (related concept)”
- “Odds are (colloquial equivalent)”
Learning
Memory Aids
Mnemonic
Think of 'Mathematical' as the strict rulebook and 'Probability' as the game of chance. Together, they are the 'rulebook for chance'.
Conceptual Metaphor
UNCERTAINTY IS A MEASURABLE SPACE. Probability turns vague 'chance' into a precise, quantifiable landscape that can be mapped and calculated.
Practice
Quiz
Which of the following best illustrates 'mathematical probability'?