Question 1118787
Let A  be the event that the disease is present in a particular person
Let B  be the event that a person tests positive for the disease<br>

The problem asks to find P(A|B), where
P(A|B) = P(B|A)*P(A) / P(B) = (P(B|A)*P(A)) / (P(B|A)*P(A) + P(B|~A)*P(~A)) <br>

In other words, the problem asks for the probability that a positive test result will be a  true positive. <br>


P(B|A) = 1-0.02 = 0.98  (person tests positive given that they have the disease)
P(A) = 0.009   (probability the disease is present in any particular person)
P(B|~A) = 0.02  (probability a person tests positive given they do not have the disease)
P(~A) = 1-0.009 = 0.991   (probability a particular person does not have the disease)<br>

P(A|B) = (0.98*0.009) / (0.98*0.009 + 0.02*0.991)
            = 0.00882 / 0.02864 = 0.30796
            which is about  {{{ highlight(0.31) }}} or {{{ highlight(31)}}} %