The risk of HIV: The risk of HIV runs high in North America. In the at-risk population,...

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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?

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P test correctly identifies carriers 95 095 P test correctly identifies the diseasefree 90 09 P atrisk population 2 002 P person is an HIV carrier atrisk population 130 P not atrisk population 1 002 098 P person is an HIV carrier not atrisk population 1300 a P a random person selected is a carrier P atrisk population P person is an HIV carrier See Answer

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