3.41 HIV in Swaziland. Swaziland has the highest HIV prevalence in the world: 25.9% of this country’s population is infected with HIV. The ELISA test is one of the first and most accurate tests for HIV. For those who carry HIV, the ELISA test is 99.7% accurate. For those who do not carry HIV, the test is 92.6% accurate.
If an individual from Swaziland has tested positive, what is the probability that he carries HIV?

The probability is 0.825 or 82.5%

Following the orange path on the tree we find 0.258223 is the probability of carrying HIV and testing positive.

That added with the 0.054834 probability of not having HIV despite testing positive is 0.313057.

The probability within testing positive and actually carrying HIV is then 0.258223/0.313057 = 0.825.

HIV Probability Tree