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 NOT having tuberculosis?

Answer:The probability of having a positive test on a non-sick person is 24.32%.Step-by-step explanation:The probability of having a POS and not having tuberculosis, can be defined as the probability of getting a false positive.The amount of positive test will be1) The positive test of sick persons[tex]P(test=pos;person=sick)=0.744*0.05=0.0372[/tex]2) The positive test of not-sick persons (false positives)[tex]P(test=pos;person=sick)=(1-0.744)*0.95=0.256*0.95=0.2432[/tex]The amount of positive test will be1) The negative test of non-sick persons[tex]P(test=neg;person=non-sick)=0.7653*0.95=0.727[/tex]2) The negative test of sick persons (false negatives)[tex]P(test=neg;person=non-sick)=(1-0.7653)*0.05=0.2347*0.05=0.0117[/tex]