Final answer:
In the context of independent events in probability, the correct formula for the probability of both events A and B occurring is the product of their individual probabilities, i.e., P(A and B) = P(A) * P(B).
Step-by-step explanation:
The subject of this question is Mathematics, specifically dealing with the calculation of probabilities for independent events. The correct formula to use when calculating the probability of two independent events A and B both occurring (denoted as P(A and B)) is the product of their individual probabilities: P(A) * P(B).
The addition rule of probability states that the probability of either of two mutually exclusive events A or B occurring (denoted as P(A or B)) is the sum of their individual probabilities minus the probability that both occur: P(A or B) = P(A) + P(B) - P(A and B).
The conditional probability P(A | B) represents the probability of event A occurring given that event B has already occurred, and if A and B are independent, it should equal P(A).For example, if the probability of event A happening is 0.3 and the probability of event B happening is 0.5, then the probability of both events A and B happening is 0.3 * 0.5 = 0.15.
Therefore, the correct answer is D) P(A and B) = P(A) * P(B).