Question

Incorrect Question 2 0 / 2 pts 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?a) 0.0373 b) 0.0127 c) 0.2230 d)0.7270

Answer 1

Solution:

Given:

the population of adults that is taking the test, 5% have tuberculosis.

Let S = the adult really has tuberculosis

thus P(S)= 5% = 0.05

and NS = Do not have tuberculosis

thus P(NS)= 1 - P(S) = 1 - 0.05 = 0.95

We also have: The test correctly identifies 74.6% of the time adults with a tuberculosis and correctly identifies those without tuberculosis 76.53% of the time.

Let POS =  the test gives a positive result

Thus we have:

P(POS | S ) = 74.6%

P(POS | S ) = 0.746

and

Let NEG =    the test gives a negative result

thus we have :

P(NEG | NS) = 76.53% = 0.7653

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

That is we have to find:

P( NEG and NS) = .............?

Using conditional rule of probability , we get:

that is:

Thus the probability of an adult getting a NEG result and truly NOT having tuberculosis = 0.7270