(10 points each) An enzyme-linked immunosorbent assay (ELISA) test is performed
ID: 3044999 • Letter: #
Question
(10 points each) An enzyme-linked immunosorbent assay (ELISA) test is performed to determine if the human immunodeficiency virus (HIV) is present in the blood of indicates HIV 99% of the time, and that the proportion of time that it correctly indicates no HIV is 99.5%. Suppose the prevalence of HIV among blood donors is known to be 1/10000 a. What proportion of blood that is donated will test positive using the ELISA test? b. What is the probability that a positive ELISA test is truly positive, that is, what proportion of individuals with positive outcomes are actually infected with HIV?Explanation / Answer
Given, P(Test positive | HIV present) = 99%
and P(Test negative | HIV absent) = 99.5%
P(Test is positive) = P(HIV present) * P(test positive | HIV present) + P(HIV absent) * P(test positive | HIV absent)
= (1/10000) * 0.99 + (1 - 1/10000) * (1 - 0.995)
= 0.0000995
b. By Bayes' theorem,
P(HIV present | Test positive ) = P(HIV present) * P(test positive | HIV present) / P(Test is positive)
= (1/10000) * 0.99 / 0.0000995 = 0.99498 (Answer)
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