Revision as of 02:17, 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> Prove that for any three events <math>A</math>, <math>B</math>, <math>C</math>, each having positive probability, and with the property that <math>P(A \cap B) > 0</math>, <math display="block"> P(A \cap B \cap C) = P(A)P(B|A)P(C|A \cap B)\ . </...")
BBy Bot
Jun 09'24
Exercise
[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]
Prove that for any three events [math]A[/math], [math]B[/math], [math]C[/math], each having positive
probability, and with the property that [math]P(A \cap B) \gt 0[/math],
[[math]]
P(A \cap B \cap C) = P(A)P(B|A)P(C|A \cap B)\ .
[[/math]]