Section 3.4: Multiplication Rule (of Probability): Basics

1. Explain the difference between sampling with replacement and sampling without replacement.
2. Explain the interpretation of a conditional probability \(P(A \mid B)\) in terms of the number of times that \(B\) occurred and the number of times \(A\) and \(B\) occurred.
3. Explain the interpretation of a conditional probability \(P(A \mid B)\) as the probability of \(A\) given knowledge of \(B\).
4. Give the definition of the conditional probability \(P(A \mid B)\) in terms of \(P(A \text{ and } B)\) and \(P(B)\).
5. Explain how to ‘factor’ \(P(A \text{ and } B)\) in terms of marginal and conditional probabilities, aka the Multiplication Rule.
6. Define the independence of two events \(A\) and \(B\) in terms of factoring the probability \(P(A \text{ and } B)\) and in terms of the conditional probabilities \(P(A \mid B)\) and \(P(B \mid A)\).

Section 3.5: Multiplication Rule (of Probability): Beyond the Basics

1. Define the complement of an event, and identify the complement of an event on a Venn Diagram.
2. Compute the probability that at least one event occurs using the probability the probability that no events occur.
3. Compute conditional probabilities from contingency tables.
4. Compute conditional probabilities given base rates and conditional probabilities using a diagram of natural frequencies.