False Positive HIV Test

Imagine an HIV test that is 95% accurate (false positive rate of 5%) and around 2% of the tested population is infected with HIV. What is the probability that you actually have HIV when your test comes back positive?


To read more about this, see the False Positive Paradox page on Wikipedia.

Posted in Brain Teasers


4 Comments on "False Positive HIV Test"

T says
October 19, 2018 @ 15:52

Please could someone explain the maths behind how to get to this solution?

Hugo Zyl says
February 9, 2020 @ 20:13

Answer: 40%

Reason: 100 people test, 2 are really positive, but 5 test positive. 2/5*100=40%

(I think so)

Jonathan says
April 2, 2020 @ 05:28

Explanation: to compute the probability that you actually have HIV if your result is positive, you want to compare the number of True Positives to the total number of positive results (True Positive + False Positive), a.k.a the True Positive Ratio.

FP = 5% of 98% that doesn’t have HIV = 4.9% of the population
TP = 2% of the population

The TPR is then TP / (TP+FP) = 29%

Theo says
December 22, 2020 @ 01:05

This reminds me of the False Positive Riddle on TED-Ed (https://m.youtube.com/watch?v=1csFTDXXULY).

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