Test for HIV. There's a false positive rate of 0.025 and a false negative rate of 0.08. Let's say a particular patient has a probability of testing positive for HIV of 0.005. The patient gets tested and it's positive. What are the chances that the patient actually has HIV?

Kenya Leonard

Kenya Leonard

Answered question

2022-07-23

Test for HIV. There's a false positive rate of 0.025 and a false negative rate of 0.08. Let's say a particular patient has a probability of testing positive for HIV of 0.005. The patient gets tested and it's positive. What are the chances that the patient actually has HIV?

Answer & Explanation

Brendon Bentley

Brendon Bentley

Beginner2022-07-24Added 11 answers

This is a typical application of Bayes formula,
P ( B | A ) = P ( A | B ) P ( B ) / ( P ( A | B ) P ( B ) + P ( A | B ¯ ) P ( B ¯ ) ) .
Here A is testing positive, B is having HIV, and B ¯ is not having HIV. P ( A | B ) is the true positive rate, the complement of the fpr .08. P ( A | B ¯ ) is the false positive rate .025. Substituting the numbers you give, P ( B | A ) = .92 .005 / ( .92 .005 + .025 .995 ) = 0.1560645.

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