2014 AIME II Problems/Problem 2
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Problem
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 
. The probability that a man has none of the three risk factors given that he doest not have risk factor A is 
, where 
and 
are relatively prime positive integers. Find 
.
