Graduate Management Admission Test (GMAT) Practice Test

In probability, how are events A and B combined if they are independent?

1. P(A) + P(B)

2. P(A) + P(B) - P(A and B)

3. P(A) x P(B)

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

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

When considering independent events in probability, the crucial aspect is that the occurrence of one event does not affect the occurrence of another event. For independent events A and B, the probability of both events occurring simultaneously—denoted as P(A and B)—is calculated by multiplying their individual probabilities. Thus, the formula used is P(A) x P(B). This multiplication reflects the definition of independence. If A and B are independent, knowing that A has occurred does not change the probability of B occurring. Because of this independence, the joint probability of both events happening together is simply the product of their individual probabilities, which supports the correctness of the answer provided. The other combinations suggested do not accurately represent the relationship between independent events. For example, adding their probabilities together would not account for their simultaneous occurrence properly, as would be necessary in the case of dependent events.