Final answer:
The General Multiplication Rule is a key concept in probability used to calculate the chance of two events occurring together. For dependent events, it involves multiplying the probability of one by the conditional probability of the other. For independent events, it is simply the product of their individual probabilities.
Step-by-step explanation:
The General Multiplication Rule is a fundamental principle in probability that is used to calculate the probability of the intersection of two events, symbolized as P(A and B). When events A and B are not independent, the probability of both A and B occurring is given by P(A and B) = P(A) × P(B|A) or P(A and B) = P(B) × P(A|B). The conditional probability, P(A|B) or P(B|A), represents the probability of one event given that another event has occurred. This rule adjusts the sample space to reflect that the outcome of one event affects the outcome of another. If events A and B are independent, the probability of both occurring simplifies to P(A and B) = P(A) × P(B), since the outcome of one event does not influence the other.
Application of the Multiplication Rule is pivotal in scenarios involving dependent events or sampling without replacement. It is contrasted with the Addition Rule, P(A or B) = P(A) + P(B) - P(A and B), which is used for calculating the probability of either one of two events occurring. Frameworks such as contingency tables or using characteristics and traits in biology are practical examples of the rule's application.