Prerequisites & Notation

This chapter builds directly on the probability-space framework from Chapter 1. The following should be fluent before proceeding.

Probability space $(\Omega, \mathcal{F}, \mathbb{P})$ : sample space, $\sigma$ -algebra, probability measure(Review ch01)
Self-check: Can you verify that a candidate function $\mathbb{P}$ satisfies the three Kolmogorov axioms?
Set operations: union, intersection, complement, difference, De Morgan's laws(Review ch01)
Self-check: Can you prove $\mathbb{P}(A \cup B) = \mathbb{P}(A) + \mathbb{P}(B) - \mathbb{P}(A \cap B)$ from the axioms?
Countable additivity and its consequences: monotonicity, continuity of $\mathbb{P}$ (Review ch01)
Self-check: If $A_n \uparrow A$ , can you explain why $\mathbb{P}(A_n) \to \mathbb{P}(A)$ ?
The Borel-Cantelli lemma (first half)(Review ch01)
Self-check: State conditions under which $\mathbb{P}(\limsup A_n) = 0$ .

Symbols introduced or prominently used in Chapter 2. See the master notation table for the full library-wide list.

Symbol	Meaning	Introduced
$\mathbb{P}(A \mid B)$	Conditional probability of $A$ given $B$	s01
$\{B_i\}_{i=1}^n$	Partition of $\Omega$ : pairwise disjoint events whose union is $\Omega$	s02
$n, k$	Trial count and success count (repeated Bernoulli trials)	s05
$p$	Success probability in a single Bernoulli trial	s05
$\binom{n}{k}$	Binomial coefficient $n!/[k!(n-k)!]$	s05