Part II — Foundations of Probability

Probability as a formal system: sample spaces and events, the axioms that govern them, and the conditioning machinery — conditional probability, Bayes' rule, independence, and the law of total probability — that everything later in the appendix leans on.

Topics

Topic	Focus
Probability Spaces	Sample spaces, events, and the structure of a probability model
Probability Axioms	The three axioms and their consequences, with discrete and continuous examples
Conditional Probability	Definition, properties, and the multiplication rule
Bayes' Rule	Inverting conditional probabilities, with a worked example
Independence	Independent events, conditional independence, and mutual independence
Law of Total Probability	Decomposing probabilities over a partition of the sample space