Graduate Management Admission Test (GMAT) Practice Test

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When dealing with probabilities, what does the term P(A and B) refer to in independent events?

P(A) + P(B)
P(A) x P(B)
P(A) - P(B)
P(A) + P(B) - P(A) x P(B)

The correct answer is: P(A) x P(B)

In probability theory, when dealing with independent events, the term P(A and B) represents the probability that both events A and B occur simultaneously. For independent events, the occurrence of one event does not affect the occurrence of the other. The fundamental rule for calculating the probability of both events happening is to multiply their individual probabilities together. This is expressed mathematically as P(A and B) = P(A) × P(B). This multiplication rule stems from the definition of independence: since the outcome of event A does not influence event B and vice versa, the overall likelihood of both occurrences is simply the product of their individual probabilities. Therefore, option B is correct as it accurately represents this concept.