Question

The probability that a married man watches a certain T.V. show is $0.6$ and the probability that a married woman watches the show is $0.5$ . The probability that a man watches the show given that his wife does watch is $0.8$ . If the probability that a wife watches the show given that her husband does watch is $k,$ then $\frac{1}{k}$ is equal to

Answer 1

$M \rightarrow $ a married man watches the T.V. show
$W \rightarrow $ a married woman watches the T.V. show
$P\left(M\right)=0.6,P\left(W\right)=0.5$
$P\left(\frac{M}{W}\right)=0.8$
$P\left(\frac{M}{W}\right)=\frac{P \left(M \cap W\right)}{P \left(W\right)}=0.8\Rightarrow P\left(M \cap W\right)=0.4$
$P\left(\frac{W}{M}\right)=\frac{P \left(W \cap M\right)}{P \left(M\right)}=\frac{0.4}{0.6}=\frac{2}{3}$