Basically, if the incidence of the disease/defect is very low, even with a super accurate test the number of false positives will swamp the number of actual cases.
So, in the case at hand, if we test an appropriate sample of 10,000 people, 9999 of them won't have the disease, and the test will correctly tell us that in 9999 * 0.999 = 9989 of of the cases. However, the test will also throw up 10 false positives. Put that together with the one actual positive in 10000, and your chances of being that one are 1/11, or a hair over 9%.
I remember reading that they gave this question to actual doctors, and like 40% of them got the wrong answer.










