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