Although the accurate determination of the proportion of false positives and false negatives produced by an important medical test are important, the probability of the following two events are of greater interest. In the following two questions, you may assume that the point estimators of false positives and false negatives are the correct values of these probabilities. The prevalence of HIV in the population of people who donate blood is thought to be around 1%.
a. Suppose a person goes to a clinic, donates blood, and the test of the AIDS virus results in a positive test result. What is the probability that the person donating blood actually is carrying HIV?
b. Suppose a person goes to a clinic, donates blood, and the test of the AIDS virus results in a negative test result. What is the probability that the person donating blood does not have HIV?