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 NEG result and truly NOT having tuberculosis?

Explanation / Answer

probability of an adult getting a NEG result and truly NOT having tuberculosis

=P(not having tuberculosis)*P(NEG result|not having tuberculosis)

=(1-0.05)*0.7653=0.727035 ~ 72.7035%

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