Final answer:
To predict the frequency of two independent events happening at the same time, we use the multiplication rule: P(A AND B) = P(A)P(B). This rule requires the events to be unrelated, meaning the outcome of one does not affect the other.
Step-by-step explanation:
The frequency of two independent events occurring simultaneously is predicted using the product rule of probabilities, i.e., P(A AND B) = P(A)P(B).
In the context of probability, an important concept is that of independent events, which are two or more events where the occurrence of one event does not influence the occurrence of the other. To calculate the probability of two independent events occurring at the same time, we use the multiplication rule. This rule states that the probability of both events A and B occurring is equal to the product of their individual probabilities, expressed as P(A AND B) = P(A)P(B). For instance, if flipping a coin and rolling a die are two independent events, the probability of flipping a tails (P(T) = 1/2) and rolling a six (P(6) = 1/6) simultaneously is calculated as P(T AND 6) = P(T)P(6) = 1/2 * 1/6 = 1/12.
This rule is fundamentally grounded in the assumption that the events are independent. In terms of conditional probability, for two events A and B, if P(B|A) = P(B), the events are independent, which means the probability of B occurring does not change even if A occurs.