The risk of HIV:
The risk of HIV runs high in North America. In the at-riskpopulation, about 1 in 30 people are HIV carriers, while in generalpopulation (people who are not at risk), 1 in 300 are. The at-riskpopulation is 2% in total in North America. Doctors have developeda test for HIV and suppose that it correctly identifies carriers95% of the time, while it correctly identifies the disease-freeonly 90%. As the test detects HIV only, you can assume that it isconditionally independent of being at risk, given carrier ornot-carrier status.
a. If a random person is sampled, what is the probability thathe/she is a carrier?
b. Given that a person has a positive test result and is not inthe at-risk population, what is the probability that he/she is acarrier?
