Ohio Assessments for Educators (OAE) Mathematics Practice Exam

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What does P(A|B) represent in probability theory?

Probability of A given B has already occurred
Probability of B given A has already occurred
Probability of A and B occurring
Probability of A or B occurring

The correct answer is: Probability of B given A has already occurred

In probability theory, P(A|B) represents the conditional probability of event A occurring given that event B has already occurred. This measure allows us to understand the likelihood of A in the context where B is a known condition. When calculating conditional probability, the focus is on the scenario where we are certain about B, and we want to know how this affects the probability of A. In contrast, the other options focus on different aspects of probability. The concept of the probability of B given A relates to a different conditional situation and does not capture the direct relationship that P(A|B) specifies. Additionally, the probability of both A and B occurring together or the probability of either A or B occurring involves different calculations and contexts altogether. Thus, P(A|B) clearly defines the relationship between A and B, emphasizing the condition that B has been satisfied before considering A.