Conditional probability: Difference between revisions

Revision as of 22:09, 19 April 2023

Revision as of 22:11, 19 April 2023

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{{Short description|ProbabilityofProbability of an event occurring, given that another event has already occurred}}

{{Probability fundamentals}}

In [[probability theory]], '''conditional probability''' is a measure of the [[probability]] of an [[Event (probability theory)|event]] occurring, given that another event (by assumption, presumption, assertion or evidence) has already occurred.<ref name="Allan Gut 2013">{{cite book |last=Gut |first=Allan |title=Probability: A Graduate Course |year=2013 |publisher=Springer |___location=New York, NY |isbn=978-1-4614-4707-8 |edition=Second }}</ref> This particular method relies on event B occurring with some sort of relationship with another event A. In this event, the event B can be analyzed by a conditional probability with respect to A. If the event of interest is {{mvar|A}} and the event {{mvar|B}} is known or assumed to have occurred, "the conditional probability of {{mvar|A}} given {{mvar|B}}", or "the probability of {{mvar|A}} under the condition {{mvar|B}}", is usually written as {{math|P(''A''{{!}}''B'')}}<ref name=":0">{{Cite web|title=Conditional Probability|url=https://www.mathsisfun.com/data/probability-events-conditional.html|access-date=2020-09-11|website=www.mathsisfun.com}}</ref> or occasionally {{math|P{{sub|''B''}}(''A'')}}. This can also be understood as the fraction of probability B that intersects with A: <math>P(A \mid B) = \frac{P(A \cap B)}{P(B)}</math>.<ref>{{Cite journal|last1=Dekking|first1=Frederik Michel|last2=Kraaikamp|first2=Cornelis|last3=Lopuhaä|first3=Hendrik Paul|last4=Meester|first4=Ludolf Erwin|date=2005|title=A Modern Introduction to Probability and Statistics|url=https://doi.org/10.1007/1-84628-168-7|journal=Springer Texts in Statistics|language=en-gb|pages=26|doi=10.1007/1-84628-168-7|isbn=978-1-85233-896-1 |issn=1431-875X}}</ref>