Recall this information from a previous lab:
the ELISA test was an early test used to screen blood donations for antibodies to HIV. A study (Weiss et. al. 1985) found that the conditional probability that a person would test positive given that they had HIV was 0.97, and the conditional probability that a person would test negative given that they did NOT have HIV was 0.926. The World Almanac gives an estimate of the probability of a person in the USA of having HIV to be 0.0026.
A. Find the theoretical conditional probability that a person has HIV given that they test positive.
You may use a tree diagram, the Bayes rule, or create a two-way table with expected counts to compute the conditional probability. Show your work.
B. In the previous lab, the conditional probability of HIV given positive test results was found for a simulated scenario. List that number and explain if it is close to the theoretical probability you found in part A.
C. Based on your theoretical and simulated results, would you recommend that this be the first and only test used to detect HIV? Why or why not?