[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]

Let [math]\Omega = \{a,b,c,d,e,f\}[/math]. Assume that [math]m(a) = m(b) = 1/8[/math] and

[math]m(c) = m(d) = m(e) = m(f) = 3/16[/math]. Let [math]A[/math], [math]B[/math], and [math]C[/math] be the events [math]A = \{d,e,a\}[/math], [math]B = \{c,e,a\}[/math], [math]C = \{c,d,a\}[/math]. Show that [math]P(A \cap B \cap C) = P(A)P(B)P(C)[/math] but no two of these events are independent.