Tesong for HU An article in the New York I imet tome time after reported mat col

Question

Tesong for HU An article in the New York I imet tome time after reported mat college students are beginning to routinely atk to be tested for the AIDS - standard test fix the HIV virus is the Elias test, which tests for the HIV it is estimated that this has a 99 8% sensitivity and a 99 8% specificity A 99.8. sensitiviry means that, in a large-scale screening test, for every 1000 people tested virus we can expert 998 people to test positive and 2 to have a false negative test A 99 8% specificity means that, in a large-scale screening test, for every 1000 people tested who do not have the vims wc can expert 998 people to have a negative test and 2 to have a false positive test. The New York Times article remarks that it is estimated that about 2 in every 100 college students have the HIV vims. Assume that a large group of randomly chosen college students, say 100.000. arc tested by the Elias test. If a student tests positive, what is the chance that this student has the HIV virus? What would this probably be for a population at high risk, where 5% of the population has the HIV virus?

Explanation / Answer

(a)

P(students has a HIV virus and is tested positive) = 0.002*0.998

P(student doesn't have a HIV virus but is tested positive) = 0.998*0.002

P(student has HIV virus | student tests positive ) = (0.002*0.998)/(0.002*0.998+0.998*0.002) = 0.50

(b)

P(student has HIV virus | student tests positive ) = (0.05*0.998)/(0.05*0.998+0.95*0.002) = 0.96

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