Answer
The probability that homes owned by single owners have swimming pool is approximately $19.81 \%$ which is more than the probability that homes owned by married couples have swimming pool as found in previous part (a).
So, the pool manufactures should go after single homeowners.
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:
$P(S|M')=\dfrac{P(M'|S)P(S)}{P(M'|S)P(S)+P(M'|S')P(S')}=\dfrac{(0.14)(0.15)}{(0.14)(0.15)+(1-0.9)(1-0.15)}$
or, $ \approx 0.1981$
or, $=19.81 \%$
Thus, we conclude the probability that homes owned by single owners have swimming pool is approximately $19.81 \%$ which is more than the probability that homes owned by married couples have swimming pool as found in previous part (a).
So, the pool manufactures should go after single homeowners.
