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Reminder: You obtain a positive test result for HIV. There is no reason to believe that...

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Basic Math

Reminder: You obtain a positive test result for HIV. There is noreason to believe that you should have a higher prior probabilityof being HIV positive than the average the average person inAustralia. In Australia, about 30,000 people out of 24 millionpeople are HIV positive. The test has a false negative rate of 0.2%(i.e., the probability of obtaining a negative result for a personwho is HIV positive is 0.002) and a false positive rate of 2.5%(i.e., the probability of obtaining a positive result for a personwho is HIV negative is 0.025). After obtaining this test result,what are the posterior odds in favour of you being HIVpositive?

A. 0.001 (this corresponds to odds of about 1 to 911 that you areHIV positive)
B. 0.015 (this corresponds to odds of about 1 to 67 that you areHIV positive)
C. 0.063 (this corresponds to odds of about 1 to 16 that you areHIV positive)
D. 0.072 (this corresponds to odds of about 1 to 14 that you areHIV positive)
E. 0.050 (this corresponds to odds of about 1 to 20 that you areHIV positive)

Answer & Explanation Solved by verified expert
4.2 Ratings (681 Votes)
Let HIV be the event that a random person is HIV positive Let N and P be the event that the person tested negative and positive respectively Probability that a random person is HIV positive PHIV    See Answer
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