Question

When two events, A and B, are independent, then P(B|A) = P(B), because knowing that A occurred does not affect the probability that B occurs. This leads to a simplified version of the multiplication rule.

What is the simplified version of the multiplication rule for independent events, and how does it apply to events A and B when they are independent?

Answer 1

The simplified multiplication rule for independent events A and B is P(A AND B) = P(A)P(B), indicating that the probability of both events occurring is the product of their individual probabilities.

Step-by-step explanation:

The simplified version of the multiplication rule for two independent events A and B is P(A AND B) = P(A)P(B). This equation expresses that the probability of both events A and B occurring together is the product of their individual probabilities. This rule applies because for independent events, the occurrence of one event does not affect the probability of the occurrence of the other event.

Therefore, when you have two independent events, you can simply multiply their probabilities to find the combined probability of both events occurring. Here's an example illustrating this principle: If you have a fair coin and a fair die, the probability of tossing a heads (P(A) = 0.5) and rolling a four (P(B) = 1/6) would be P(A AND B) = P(A)P(B) = (0.5)(1/6) = 1/12. Since the outcome of the coin toss does not affect the die roll, these events are independent, and the multiplication rule applies straightforwardly.