Swaziland has the highest HIV prevalence in the world: 25.9% of this country’s population is infected...

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 they carry HIV

Expert Solution

P(infected with HIV) = 0.259

P(tested positive | infected with HIV) = 0.997

P(tested negative | didn't infect with HIV) = 0.926

P(tested positive | didn't infect with HIV) = 1 - P(tested negative | didn't infect with HIV) = 1 - 0.926 = 0.074

P(tested positive) = P(tested positive | infected with HIV) * P(infected with HIV) + P(tested positive | didn't infect with HIV) * P(didn't infect with HIV)

= 0.997 * 0.259 + 0.074 * (1 - 0.259)

= 0.3131

P(carry HIV | tested positive) = P(tested positive | infected with HIV) * P(infected with HIV) / P(tested positive)

= 0.997 * 0.259 / 0.3131

= 0.8247

orchestra answered 2 years ago

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