Revision as of 03:17, 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> Suppose that <math>A</math> and <math>B</math> are events such that <math>P(A|B) = P(B|A)</math> and <math>P(A \cup B) = 1</math> and <math>P(A \cap B) > 0</math>. Prove that <math>P(A) > 1/2</math>.")
BBy Bot
Jun 09'24
Exercise
[math]
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Suppose that [math]A[/math] and [math]B[/math] are events such that [math]P(A|B) = P(B|A)[/math] and [math]P(A \cup B) = 1[/math] and [math]P(A \cap B) \gt 0[/math]. Prove that [math]P(A) \gt 1/2[/math].