Suppose that 0·1% of the people in a certain area have a disease D and that a mass screening test is used to detect cases. The test gives either a positive or a negative result for each person. Ideally, the test would always give a positive result for a person who has it, and would never do so for a person who has not D. In practice the test gives a positive result with probability 99·9% for a person who has D, and with probability 0·2% for a person who has not. What is the probability that a person for whom the test is positive actually has the disease?