Problem 2: The New York State Health Department reports a 10% rate of the HIV vi

Question

Problem 2: The New York State Health Department reports a 10% rate of the HIV virus for the-at population Under certain conditions, a preliminary screening test for the HIV virus is accurate 95% of the time. (Subjects are not told that they are HIV infected until additional tests verify the results.) If someone is randomly selected from the at-risk population, what is the probability tharthey have the HIv virus if it is known that they have tested positive in the initial screening? 10 Points -risk"

Explanation / Answer

Ans:

Given that

P(HIV)=0.1

P(positive/HIV)=0.95

P(negative/no HIV)=0.95

P(positive/no HIV)=1-0.95=0.05

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

=0.95*0.1+0.05*0.9

=0.095+0.045

=0.14

Use Bayes Rule:

P(HIV/positive)=P(positive/HIV)*P(HIV)/P(positive)

=0.95*0.1/0.14

=0.095/0.14

=0.6786

  

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