Discrete Mathematics and Its Applications, Seventh Edition

Published by McGraw-Hill Education
ISBN 10: 0073383090
ISBN 13: 978-0-07338-309-5

Chapter 7 - Section 7.3 - Bayes' Theorem - Exercises - Page 475: 2



Work Step by Step

To find $p(E|F)$, or the probability that event $E$ occurs if the event $F$ occurs, we use Bayes' Theorem, which states that $p(E|F)=p(F|E)p(F)p(E)$. $p(E)=\frac{2}{3},p(F)=\frac{3}{4}$, and $p(F|E)=\frac{5}{8}$, so $p(E|F)=\frac{\frac{5}{8}\frac{3}{4}}{\frac{2}{3}}=\frac{45}{64}$. This fraction is already in its simplest form.
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