# 2.23 HIV in Swaziland, Swaziland has the highest HIV prevalence in the world: 25.9% of this...

2.23 HIV in Swaziland, Swaziland has the highest HIV prevalence in the world: 25.9% of this country's population is infected with HIV.66 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 IllV. Lhe ksı is 9%.6% aocurate. If an İndividual frun Swaziland has ksiexl IX2ilLive, whai. is the probability that he carries HIV?

Given,

P(HIV) = 0.259

So,

P(Not HIV) = 1 - 0.259 = 0.741

P(Test positive |HIV) = 0.997

P(Test negative |Not HIV) = 0.926

Hence,

P(Test positive |Not HIV) = 1 - 0.926 = 0.074

Using Baye's theorem,

P(HIV |Test positive)

$= \frac{P(Test Positive |HIV)P(HIV)}{P(Test Positive |HIV)P(HIV) + P(Test Positive |Not HIV)P(Not HIV)}$

$= \frac{0.997*0.259}{0.997*0.259 + 0.074*0.741}$

= 0.8248

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