Tests for tuberculosis like all other diagnostic tests are not perfect. QFT-G is

Question

Tests for tuberculosis like all other diagnostic tests are not perfect. QFT-G is one of such tests for tuberculosis. Suppose that for the population of adults that is taking the test, 5% have tuberculosis. The test correctly identifies 74.6% of the time adults with a tuberculosis and correctly identifies those without tuberculosis 76.53% of the time. Suppose that POS stands for the test gives a positive result and S means that the adult really has tuberculosis. What is the probability of an adult getting a POS result and truly have tuberculosis?

Explanation / Answer

(POS result and truly having tuberculosis) = P(POS result is having tuberculosis) x P(truly having tuberculosis)

0.746 x 0.05

= 0.0373

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