Question 2
Arnold is studying the prevalence of three health risk factors, denoted by $A,$ $B,$ and $C,$ within a population of men. For each of the three factors, the probability that a randomly selected man in the population has only this risk factor (and none of the others) is $0.1.$ For any two of the three factors, the probability that a randomly selected man has exactly these two risk factors (but not the third) is $0.14.$ The probability that a randomly selected man has all three risk factors, given that he has $A$ and $B,$ is $\frac{1}{3}.$ The probability that a man has none of the three risk factors given that he does not have risk factor $A$ is $\frac{p}{q},$ where $p$ and $q$ are relatively prime positive integers. Find $p + q.$