5. (7 points) The Rapid Test is used to determine whether some- one has HIV (the

Question

5. (7 points) The Rapid Test is used to determine whether some- one has HIV (the virus that causes AIDS). The false- positive and false-negative rates are.047 and.090, 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?

Explanation / Answer

Ans:

Given that

P(positive/no HIV)=0.047

P(negative/HIV)=0.09

P(positive//HIV)=1-0.09=0.91

P(HIV)=0.005

P(no HIV)=1-0.005=0.995

P(positive)=P(positive/HIV)*P(HIV)+P(positive/no HIV)*P(no HIV)

=0.91*0.005+0.047*0.995

=0.0513

Now,we have to find:

P(HIV/positive)=P(positive/HIV)*P(HIV)/P(positive)=0.91*0.005/0.0513=0.0887

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