[math] \newcommand{\NA}{{\rm NA}} \newcommand{\mat}[1]{{\bf#1}} \newcommand{\exref}[1]{\ref{##1}} \newcommand{\secstoprocess}{\all} \newcommand{\NA}{{\rm NA}} \newcommand{\mathds}{\mathbb}[/math]

• For events [math]A_1, \dots, A_n[/math], prove that
  [[math]] P(A_1 \cup \cdots \cup A_n) \leq P(A_1) + \cdots + P(A_n)\ . [[/math]]
• For events [math]A[/math] and [math]B[/math], prove that
  [[math]] P(A \cap B) \geq P(A) + P(B) - 1. [[/math]]