Ohio Assessments for Educators (OAE) Mathematics Practice Exam

The probability of a compound event that involves the occurrence of at least one of two events, A or B, is expressed mathematically as P(A or B) = P(A) + P(B) - P(A and B). This formula accounts for the overlap between the two events by subtracting the probability of both A and B occurring simultaneously, which is represented by P(A and B), to prevent double-counting.

When calculating the probability of either A or B happening, simply adding P(A) and P(B) would overstate the likelihood when both events can occur together. For example, if you have two events where both can happen at the same time, the probability of their joint occurrence needs to be subtracted to achieve an accurate probability of the union of the two events.

This is a fundamental concept in probability theory known as the principle of inclusion-exclusion, which helps ensure that the probability measure reflects the true likelihood of compound events without redundancy. Understanding this formula is crucial for anyone studying probability, as it provides the basis for more complex probability calculations involving multiple events.