Conditional probability
Conditional Probability
Conditional probability is a term used in probability theory and statistics to refer to the probability of an event given that another event has occurred. It is often denoted as P(A|B), which is read as "the probability of A given B."
Pronunciation
/kənˈdɪʃənəl prɒbəˈbɪlɪti/
Etymology
The term "conditional probability" is derived from the English words "conditional," meaning dependent on a condition, and "probability," which refers to the likelihood of an event occurring. The concept has been a part of probability theory since its inception in the 17th century.
Definition
In probability theory, the conditional probability of an event A given that another event B has occurred is defined as the ratio of the probability that both events A and B occur to the probability that B occurs. Mathematically, this is expressed as:
P(A|B) = P(A ∩ B) / P(B)
where:
- P(A|B) is the conditional probability of A given B,
- P(A ∩ B) is the probability of both A and B occurring,
- P(B) is the probability of B occurring.
Related Terms
- Probability Theory: The branch of mathematics that deals with the analysis of random phenomena.
- Statistics: The discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
- Event (probability theory): An outcome or defined collection of outcomes of a random experiment or process.
- Bayes' Theorem: A principle in probability theory and statistics that describes how to update the probabilities of hypotheses when given evidence.
See Also
External links
- Medical encyclopedia article on Conditional probability
- Wikipedia's article - Conditional probability
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