Ohio Assessments for Educators (OAE) Mathematics Practice Exam

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How is the probability of two independent events A and B occurring calculated?

P(A) + P(B)
P(A) × P(B)
P(A) × P(B|A)
P(A) × P(A|B)

The correct answer is: P(A) × P(B)

The calculation of the probability of two independent events, A and B, occurring is achieved by multiplying their individual probabilities together. This is based on the fundamental principle of probability that states if two events are independent, the occurrence of one does not affect the occurrence of the other. In mathematical terms, the probability of both events A and B happening is represented as P(A and B) = P(A) × P(B). Since A and B are independent, knowing that A has occurred does not change the probability of B occurring, which allows for this multiplication. This principle is distinct from other options that propose different methods of calculating probabilities. For example, adding the probabilities of the two events assumes that the events are mutually exclusive, which is not the case when dealing with independent events. Furthermore, the other options involving conditional probabilities suggest relationships between A and B that do not exist in independent cases. Thus, multiplying the probabilities of A and B is the correct and applicable method for calculating the joint probability of independent events.