conditional probability: meaning, definition, pronunciation and examples
C1+Academic / Technical / Formal
Quick answer
What does “conditional probability” mean?
The probability of an event occurring given that another event has already occurred.
Audio
Pronunciation
Definition
Meaning and Definition
The probability of an event occurring given that another event has already occurred.
A fundamental concept in probability theory and statistics quantifying how the likelihood of one outcome changes when another outcome is known or assumed.
Dialectal Variation
British vs American Usage
Differences
No significant lexical differences. The term is identical in both varieties.
Connotations
Purely technical/mathematical; no regional connotative differences.
Frequency
Equally frequent in academic and technical contexts in both regions.
Grammar
How to Use “conditional probability” in a Sentence
The conditional probability of [EVENT A] given [EVENT B] is...We need to compute the conditional probability that...P(A|B) denotes the conditional probability...Using Bayes' theorem, the conditional probability can be updated.Vocabulary
Collocations
Examples
Examples of “conditional probability” in a Sentence
verb
British English
- We must condition the probability on the observed data.
- The model conditions the likelihood of failure on temperature.
American English
- You need to condition the probability on the prior information.
- The algorithm conditions the forecast on real-time inputs.
adverb
British English
- The events are conditionally probable based on the initial state.
- The result was derived conditionally, assuming the hypothesis was true.
American English
- The variable is conditionally probable given the parameters.
- We can think of it conditionally, relying on the first event's outcome.
adjective
British English
- The conditional probability analysis yielded new insights.
- They worked with a conditional probability framework.
American English
- The conditional probability calculation is central to the theorem.
- We used a conditional probability approach for the risk assessment.
Usage
Meaning in Context
Business
Used in risk assessment, forecasting, and customer behavior modeling (e.g., 'The conditional probability of a loan default given a credit score drop').
Academic
Core concept in statistics, machine learning, and quantitative social sciences.
Everyday
Rarely used explicitly; the concept appears in reasoning about chance (e.g., 'What are the chances it rains, since the sky is dark?').
Technical
Precise mathematical definition: P(A|B) = P(A∩B) / P(B), provided P(B) > 0.
Vocabulary
Synonyms of “conditional probability”
Neutral
Weak
Vocabulary
Antonyms of “conditional probability”
Watch out
Common Mistakes When Using “conditional probability”
- Confusing P(A|B) with P(B|A) (the prosecutor's fallacy).
- Forgetting that P(B) must not be zero in the denominator.
- Using it for independent events where P(A|B) = P(A).
- Treating 'given' as a temporal sequence rather than a logical condition.
FAQ
Frequently Asked Questions
Unconditional (or marginal) probability P(A) considers the likelihood of A in the entire sample space. Conditional probability P(A|B) considers the likelihood of A only within the restricted sample space where B has occurred.
It is written as P(A|B), read as 'the probability of A given B'. The vertical bar '|' means 'given' or 'conditioned on'.
No. Like all probabilities, a conditional probability value must lie between 0 and 1 inclusive, provided it is a valid probability measure on the conditioned sample space.
Medical diagnostics (e.g., the probability of having a disease given a positive test result), machine learning (e.g., Naive Bayes classifiers), and finance (e.g., the probability of default given a change in interest rates).
The probability of an event occurring given that another event has already occurred.
Conditional probability is usually academic / technical / formal in register.
Conditional probability: in British English it is pronounced /kənˌdɪʃ.ən.əl ˌprɒb.əˈbɪl.ə.ti/, and in American English it is pronounced /kənˌdɪʃ.ən.əl ˌprɑː.bəˈbɪl.ə.t̬i/. Tap the audio buttons above to hear it.
Phrases
Idioms & Phrases
- “The die is loaded (figurative for a situation with altered conditional probabilities)”
Learning
Memory Aids
Mnemonic
CONDITIONAL PROBABILITY: The chance is CONDITIONED on something else already happening. Think of a CONDITION in an 'if-then' statement for likelihood.
Conceptual Metaphor
PROBABILITY IS A MEASUREMENT TOOL (like a ruler for uncertainty); CONDITIONAL PROBABILITY IS A FILTERED MEASUREMENT (like using a magnifying glass on a specific part of the measurement).
Practice
Quiz
Which formula correctly defines the conditional probability P(A|B)?