Chapter 7 - Section 7.6 - Bayes' Theorem and Applications - Exercises - Page 519: 17

$0.71$

According to Bayes' theorem: $P(F'|T')=\dfrac{P(T|F')P(F')}{P(T|F')P(F')+P(T|F)+P(F')}~~~~~~~~(1)$ Here, we have $P(T|F)=50 \%=0.5 \\ P(F)=45 \% =0.45 \\ P(T|F')=1$ Now, we will now use formula (1) and the given data to obtain: $P(F'|T')=\dfrac{P(T|F')P(F')}{P(T|F')P(F')+P(T|F)+P(F')}=\dfrac{(1)(1-0.45)}{(1)(1-0.45)+(0.5) (0.45)}$ or, $ \approx 0.71$