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# hw02 - hw02 ChE 132C due Jan.21 2011 1 HIV test example...

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hw02 ChE 132C due Jan.21 , 2011 1) HIV test example revisited. The test is positive for 99.99% of those who are infected. The test is also positive for 0.02% of those who are not infected. For a population where only 1/10000 people are infected, we showed that if a randomly selected person tests positive he has a 1/3 chance of being infected. This seems remarkably small for such an accurate test, but recall that false positives are more common than true positives. a) Repeat the analysis for a population where 1/100 are infected. b) Now return to the population where 1/10000 are infected. Our patient who just tested positive decides to take a second type of test. Within groups where everyone is infected the second test is independent of the first test. The second test is also independent of the first test outcome within groups where everyone is known to be uninfected. If our patient tests positive again in the second test, what is the probability that he is infected?
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