Answer:
The correct option is (B) 0.173.
Step-by-step explanation:
The law of total probability states that:

The conditional probability of an event <em>A</em> given that another event <em>B</em> has already occurred is:

Then the probability of intersection of A and B is:

Denote the events as follows:
<em>H</em> = a man died from causes related to heart disease.
<em>X</em> = a man had at least one parent who suffered from heart disease
The information provided is:

The probability that a man randomly selected from this group died of causes related to heart disease, given that neither of his parents suffered from heart disease is,
.
Compute the value of
as follows:

![\frac{210}{937}=[\frac{102}{312}\cdot \frac{312}{937}]+[P(H|X^{c})\cdot (1-\frac{312}{937})]\\\\\frac{210}{937}-\frac{102}{937}=[P(H|X^{c})\cdot \frac{625}{937}]\\\\\frac{108}{937}=P(H|X^{c})\cdot \frac{625}{937}\\\\P(H|X^{c})=\frac{108}{937}\times \frac{937}{625}\\\\P(H|X^{c})=0.1728\\\\P(H|X^{c})\approx 0.173](https://tex.z-dn.net/?f=%5Cfrac%7B210%7D%7B937%7D%3D%5B%5Cfrac%7B102%7D%7B312%7D%5Ccdot%20%5Cfrac%7B312%7D%7B937%7D%5D%2B%5BP%28H%7CX%5E%7Bc%7D%29%5Ccdot%20%281-%5Cfrac%7B312%7D%7B937%7D%29%5D%5C%5C%5C%5C%5Cfrac%7B210%7D%7B937%7D-%5Cfrac%7B102%7D%7B937%7D%3D%5BP%28H%7CX%5E%7Bc%7D%29%5Ccdot%20%5Cfrac%7B625%7D%7B937%7D%5D%5C%5C%5C%5C%5Cfrac%7B108%7D%7B937%7D%3DP%28H%7CX%5E%7Bc%7D%29%5Ccdot%20%5Cfrac%7B625%7D%7B937%7D%5C%5C%5C%5CP%28H%7CX%5E%7Bc%7D%29%3D%5Cfrac%7B108%7D%7B937%7D%5Ctimes%20%5Cfrac%7B937%7D%7B625%7D%5C%5C%5C%5CP%28H%7CX%5E%7Bc%7D%29%3D0.1728%5C%5C%5C%5CP%28H%7CX%5E%7Bc%7D%29%5Capprox%200.173)
Thus, the probability that a man randomly selected from this group died of causes related to heart disease, given that neither of his parents suffered from heart disease is 0.173.
The correct option is (B).