Answer
$14.43 \%$
Work Step by Step
According to Bayes' theorem:
$P(S|M)=\dfrac{P(M|S)P(S)}{P(M|S)P(S)+P(M|S')P(S')}~~~~~~~~(1)$
Here, we have
$ P(M|S)=0.86\\ P(M'|S)=0.14\\ P(S)=0.15$
Now, we will now use formula (1) and the given data to obtain:
$P(S|M)=\dfrac{P(M|S)P(S)}{P(M|S)P(S)+P(M|S')P(S')}=\dfrac{(0.86)(0.15)}{(0.86)(0.15)+(0.9)(1-0.15)}$
or, $ \approx 0.1443$
or, $=14.43 \%$
Thus, we conclude the probability that homes owned by married couples have swimming pool is approximately $14.43 \%$.
