The tests done to determine if someone is HIV positive are called Enzyme immunoassay orEIA tests. The test screens a blood sample for the presence of antibodies to HIV. Like mosttests, this test is not perfect. The table below shows the approximate probabilities of positiveand negative EIA tests when the blood does and does not actually contain the HIV antibodies.Long range studies have shown that only 2% of the population actually has the HIVantibodies.Test Result Positive NegativeAntibodies Present 0.9985 0.0015Antibodies NotPresent 0.006 0.994a) Explain in context all four values in the table. That is, what does each of them actuallymean?Construct a tree diagram to answer the following questions. The first two choices of the treeshould be whether or not the antibodies are present. The second choice should be the testresult. (What is the probability split for the first choice?)b) What is the probability that a person without HIV will have a test come out positive (this iscalled a false-positive)?c) What is the probability that a person with HIV will have a test come out negative (this iscalled a false negative)?d) What is the probability that a person with HIV will have a test come out positive?