The tests done to determine if someone is HIV positive are called Enzyme immunoassay or EIA tests. The test screens a blood sample for the presence of antibodies to HIV. Like most tests, this test is not perfect. The table below shows the approximate probabilities of positive and 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 HIV antibodies.

Question

Test Result Positive Negative
Antibodies Present 0.9985 0.0015
Antibodies Not Present 0.006 0.994

a) Explain in context all four values in the table. That is, what does each of them actually mean? I have 99.85%,0.6%,0.15% and 99.4%

Construct a tree diagram to answer the following questions. The first two choices of the tree should be whether or not the antibodies are present. The second choice should be the test result. (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 is called a false-positive)?
c) What is the probability that a person with HIV will have a test come out negative (this is called a false negative)?
d) What is the probability that a person with HIV will have a test come out positive?