A pharmaceutical company is considering new HIV test. It finds out that the test has a false positive rate of 5% (the probability that someone tests positive for HIV even though he or she doesn't have the virus), and a false negative rate of 1% (the probability that someone tests negative for HIV even though he or she does have virus). Assume that 1% of the population is infected.
a.) Determine the probability that a randomly chosen person both has the virus and tests positive?
b.) Compute the probability that the randomly chosen person doesn't have the virus but tests positive anyway?
c.) Calculate the probability that a randomly chosen person that tested positive, actually has HIV?