[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]

If [math]A[/math], [math]B[/math], and [math]C[/math] are any three events, show that

[[math]] \begin{array}{ll} P(A \cup B \cup C) &= P(A) + P(B) + P(C) \\ &\ \ -\, P(A \cap B) - P(B \cap C) - P(C \cap A) \\ &\ \ +\, P(A \cap B \cap C)\ . \end{array} [[/math]]