The rapid test is used to determine whether someone has hiv, Ask an Expert

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The Rapid Test is used to determine whether someone has HIV (the virus that causes AIDS). The false-positive and false-negative rates are 0.027 and 0.08, respectively. A physician has just received the Rapid Test report that his patient tested positive. Before receiving the result the physician assigned his patient to the low-risk group (defined on the basis of several variables) with only a 0.5% probability of having HIV. What is the probability that the patient actually has HIV? Please show your working.

(A) 8.76%

(B) 14.62%

(D) 42.96%

(E) 69.11%

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Statistics and Probability, Statistics

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