Question

Consider the following:  

      Enzyme immunoassay (EIA) tests are used to screen blood specimens for the presence of antibodies to HIV,  

      the virus that causes AIDS. Antibodies indicate the presence of the virus. The test is quite accurate but is

      not always correct. Suppose that 1% of a large population carries antibodies to HIV in their blood. Of

      those that carry the HIV antibodies in their blood, 99.85% will have a positive test result and 0.15% will

      have a false-negative test result. Of those that do not carry the HIV antibodies in their blood, 99.4% will

      have a negative test result and 0.60% will have a false-positive test result.

1. Draw a tree diagram for selecting a person from this population and testing his or her blood.

b) Construct a probability table that shows the probabilities for individuals in this population with    

respect to the presence of antibodies and test results.

Answer 1

a)

b)  

From a population 99% don’t have HIV antibodies among them 99.85% will have positive result and 0.15% will have negative result. On the other hand 1% of total population don’t have HIV antibodies and 0.60% of them will have the positive result and 99.40% will have negative result.

Now,

Then the probability for a individual among the population for having the positive result is,

     

And, the probability for a individual among the population for having the negative result is,