Chapter 2: General Rules of Probability

1. State the three main mathematical objects used in probability theory.
2. State the three axioms of probability theory.
3. Relate intersection, union, and complementation to logical statements “AND”, “INCLUSIVE OR”, and “NOT”.
4. Use Venn diagrams to reason about events and their probabilities.
5. State the Inclusion-Exclusion Principle for \(n\) events, and use the Inclusion-Exclusion Principle to compute probabilities of unions of events.
6. State the definitions of conditional probability.
7. Recognize conditional probability problems from ‘of those,’ ‘given that,’ and other key words.
8. Use repeated applications of the definition of conditional probability to ‘factor’ the probability of the intersection of events.
9. State what it means for a collection of \(k\) events to be (mutually) independent, and use this independence to simplify probability calculations.
10. State what it means for a collection of sets to form a partition of some superset.
11. State the law of total probability, and sketch a Venn diagram where the law of total probability applies.
12. Use Bayes’ Theorem to ‘flip’ the direction of conditioning.