Testing for HIV. An article in the New York Times some time ago reported thatcollege students are beginning to routinely ask to be tested for the AIDS virus. Thestandard test for the HIV virus is the Elias test, which tests for the HIV antibodies. It isestimated that this has a 99.8% sensitivity and a 99.8% specificity. A 99.8% sensitivitymeans that, in a large-scale screening test, for every 1000 people tested who have thevirus we can expert 998 people to test positive and 2 to have a false negative test. A99.8% specificity means that, in a large-scale screening test, for every 1000 people testedwho do not have the virus we can expert 998 people to have a negative test and 2 to havea false positive test.(a) The New York Times article remarks that it is estimated that about 2 in every 1000college students have the HIV virus. Assume that a large group of randomlychosen college students, say 100,000, are tested by the Elias test. If a student testspositive, what is the chance that this student has the HIV virus?(b) What would this probably be for a population at high risk, where 5% of thepopulation has the HIV virus?