Section 2.4: Conditional Probability

1. Define the conditional probability of an event \(A\) given an event \(B\): \(P(A \mid B)\)
2. Identify conditional probabilities using keywords such as if and given.
3. Explain how a conditional probability is a regular probability with a reduced sample space.
4. State and use the product rule to factor probabilities of events constructed as intersections (“ANDs”) of other events.
5. Define a partition of a set.
6. Define a partition of a sample space.
7. State the Law of Total Probability, and use the law to solve problems given the relevant information.
8. State Bayes’ Theorem, and use Bayes’ Theorem to solve problems given the relevant information.
9. Construct a tree diagram as a visual representation of the product rule for outcomes that occur in stages, and use tree diagrams to reason about the probabilities of sequences of events.