The health department reports a 1% rate of the HIV virus for the "at-risk" population. Under certain conditions, a preliminary screening test for the HIV virus is correct 90% of the time. One person is randomly selected from the at-risk population.
a. What is the probability that the selected person has the HIV virus if it is known that this person has tested positive in the initial screening?
b. What is the probability that the selected person has the HIV virus if it is known that this person has tested negative in the initial screening?