Revision as of 03:16, 9 June 2024 by Bot (Created page with "<div class="d-none"><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></div> 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 =...")
BBy Bot
Jun 09'24
Exercise
[math]
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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.