MathDB

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 as 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 two of 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

\tfrac{1}{3}

. The probability that a man has none of the three risk factors given that he does not have risk factor A is

\tfrac{p}{q}

, where

p

and

q

are relatively prime positive integers. Find

p+q

Problem Statement