The word "and" in probability implies that we use the ______ Rule.

Verified step by step guidance

1. Understand that in probability, the word "and" indicates that we are interested in the probability of two events happening together.
2. Recall that the rule used to find the probability of two events both occurring is called the Multiplication Rule.
3. The Multiplication Rule states that for two events A and B, the probability of both A and B occurring is given by \(P(A \text{ and } B) = P(A \cap B)\).
4. If the events are independent, this simplifies to \(P(A \cap B) = P(A) \times P(B)\), meaning the probability of both events is the product of their individual probabilities.
5. If the events are dependent, the rule adjusts to \(P(A \cap B) = P(A) \times P(B|A)\), where \(P(B|A)\) is the conditional probability of B given A has occurred.

Key Concepts

Multiplication Rule

The multiplication rule in probability is used to find the probability of two events occurring together, indicated by the word 'and'. It states that the probability of both events A and B happening is the product of the probability of A and the probability of B given A.

Independent and Dependent Events

Understanding whether events are independent or dependent is crucial when applying the multiplication rule. For independent events, the probability of both occurring is the product of their individual probabilities. For dependent events, the probability of the second event depends on the outcome of the first.

Conditional Probability

Conditional probability measures the likelihood of an event occurring given that another event has already occurred. It is essential for calculating the multiplication rule when events are dependent, as it adjusts the probability of the second event based on the first event's outcome.