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 having tuberculosis?

Answer 1

Answer:

the probability of an adult getting a NEG result and truly having tuberculosis is 0.0127

Step-by-step explanation:

S = the adult really has tuberculosis.

S' = complement of S = the adult does not has tuberculosis.

POS = the test gives a positive result

P(S)= 0.05

P(POS | S)=0.746

P(NEG | S')= 0.7653

this is an intersection because the "and" word

P(NEG ∩ S) =  P(NEG| S)*P(S)=(1-P(POS | S))*P(S)=(1-0.746)*0.05=0.0127