Assume that .2% of the populate is HIV positive. HIV tests, like other lab tests, are not perfect. Of those who are HIV negative, 1.5% will actually test positive. Of the those who are positive, .3% will test negative. Use this information to answer the following questions.

a. What is the probability of being HIV positive AND testing positive?

b. What is the probability of being HIV positive OR testing positive?

c. What is the probability that the test is negative given that you are HIV positive?

d. What is the probability that you are HIV negative if your test was positive?

e. What is the probability of a FALSE positive? That is, what is the probability that you test positive when you are in fact HIV negative?

f. What is the probability of a FALSE negative? That is, what is the probability that you test negative when you are HIV positive?

g. Why do you think a FALSE positive is greater than a FALSE negative? Do you think other medical tests are designed this way? Why?

h. Calculate the Specificity of this test and compare it to the Sensitivity of the test (you already calculated the Sensitivity). What is the importance of these two values?