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UPSC ESE 2024 General Studies and Engineering Aptitude

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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 D , and would never do so for a person who has not. 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 ?

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