Ohio Assessments for Educators (OAE) Mathematics Practice Exam

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The formula P(A) × P(B|A) is used to determine which type of events?

Dependent events
Independent events
Mutually exclusive events
Correlated events

The correct answer is: Dependent events

The formula P(A) × P(B|A) is specifically used to calculate the probability of two dependent events occurring. In this context, P(A) represents the probability of event A happening, while P(B|A) denotes the probability of event B occurring given that event A has already occurred. This relationship illustrates that the occurrence of event A has some influence on the probability of event B. When two events are dependent, the outcome of one event affects the likelihood of the other, which is precisely why this formula incorporates the conditional probability of B given A. Hence, this approach is essential for appropriately calculating probabilities in scenarios where events are not independent. On the other hand, independent events would utilize the formula P(A) × P(B) because the occurrence of A does not affect the occurrence of B. Mutually exclusive events cannot occur at the same time, and for correlated events, a different set of probability measures is generally used rather than this direct multiplication involving dependence.