Application of Bayes’ Theorem. Recall that Bayes’ Theorem says: P (A|B) = P (B|A)P (A)/P (B|A)P (A) + P (B|notA)P (notA)
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 they have HIV was 0.984 and the conditional probability that a person would test negative given they did not have HIV was 0.929. The World Almanac gives an estimate of the probability of a person 15 years or older in the United States of America having HIV of 0.004.
1. Suppose a random person is tested and they test positive. What is the conditional probability that this person has HIV given that they test positive?
2. Are you surprised by your answer? What implications does this have for policies of mandatory testing?
A. No; if the whole population tested we would see alot of false negatives.
B. Yes; if the whole population tested we would see alot of false positives.
C. No; the test is specific, everyone should be tested.
D. Yes; the test is specific, everyone should be tested.
3. Suppose 12,000 random people are tested. How many of them do you expect to actually have HIV people.
4. Of those with HIV, how many do you expect to test positive?
A. About 58 or 59.
B. About 1.
C. About 66 or 67.
D. About 70 or 71.