Question

Question: The New York State Health Department reports a 10% rate of the HIV virus for the “at-risk” population. Under certain conditions, a preliminary screening test for the HIV virus is correct 95% of the time. (Subjects are not told that they are HIV infected until additional tests verify the results.) If someone is randomly selected from the at-risk population, what is the probability that they have the HIV virus if it is known that they have tested positive in the initial screening? 10. HIV Use the same data from Exercise 9. If someone is randomly selected from the at-risk population, what is the probability that they have the HIV virus if it is known that they have tested negative in the initial screening?

a) What is the probability that selected person has the HIV virus if it is known that they tested positive in the initial screening?

b) What is the probability that selected person tests positive in the initial screening if is known that this person has the HIV virus?

c) What is the probability that selected person has the HIV virus if it is known that he tested negative in the initial screening?

d) What is the probability that selected person tests negative in the initial screening if it is known that he has the HIV virus?