In probability, how do you calculate the likelihood of independent events occurring together?

To determine the likelihood of independent events occurring together, the correct formula is the multiplication of their individual probabilities. When two events, A and B, are independent, the occurrence of one does not affect the occurrence of the other. Therefore, the probability of both events happening at the same time, or the joint probability, is calculated using the product of their individual probabilities.

This can be expressed mathematically as P(a and b) = P(a) * P(b). For instance, if the probability of event A occurring is 0.5 and the probability of event B occurring is 0.3, the probability of both A and B occurring together is 0.5 * 0.3, which equals 0.15. This principle of multiplication for independent events underpins many statistical analyses and real-world applications, reinforcing the idea that the occurrence of one event does not change the likelihood of the other occurring.

Other choices either reflect incorrect methods of probability computation or do not pertain to the joint occurrence of independent events.