Bayess rule was applied to the problem of HIV testing in The American Statistician (Aug. 2008). In
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a. Find the probability of interest for a North American by using Bayes’s rule.
b. In East Asia, the probability of a person having HIV is only .001. Find the probability of interest for an East Asian by using Bayes’s rule. (Assume that both the sensitivity and specificity of the test are .99.)
c. Typically, if one tests positive for HIV, a follow-up test is administered. What is the probability that a North American has HIV given that both tests are positive? (Assume that the tests are independent.)
d. Repeat part c for an East Asian.
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