Refer to Exercises 10.7 and 10.8. Although the accurate determination of the proportions of false positives and

Question:

Refer to Exercises 10.7 and 10.8. Although the accurate determination of the proportions of false positives and false negatives produced by an important medical test is important, the probabilities 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 the AIDS virus in the population of people who donate blood is thought to be around 2%.
a. Suppose a person goes to a clinic and 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 the AIDS virus?
b. Suppose a person goes to a clinic and 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 the AIDS virus?