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blackboard.boisestate.edu 1,2, 3, Bully HBO GO. It's HBO. Question Completion Status: QUESTION 42 The Chembio test can be used to screen HIV-infected patients for hepatitis C. According to the CDC, the prevalence dof HIV and HCV co-infection is approximately 25%. Use the outcome from the screening test (results below) for the Chembio HCV Rapid Test to determine the likeihood that a randomly selected HIV infected patient will also have an HCV infection given their Chembio HCV Rapid Test returns a positive result. That is, determine P(HCV Infection | Positive Chembio HCV Test), Round answer to nearest tenth of a percent (ie, 79.2%). Positive Chembio Test Result Negative Chembio Test Result 42 Hepatitis C No Hepatitis C 335 14 1153 QUESTION 43

Explanation / Answer

Using Baye's rule,

P(HCV / positive chembio) x P (positive chembio) = P (HCV and positive chembio).

It is given that P(HCV) = probability of having HCV infection = 25% = 0.25

So probability of not having HCV infection = 1-0.25 = 0.75

P (HCV and positive chembio) = P(positive chembio /HCV) x P(HCV) = (335/(335+42)) x 0.25 = (335/377) x 0.25= 0.222

P(positive chembio) = P(positive chembio /HCV) x P (HCV) + P (positive chembio /No HCV) x P (No HCV) = (335/(335+42)) x 0.25 + (14/(14+1153)) x 0.75 = 0.2221 + 0.009 =0.231

Hence, P(HCV / positive chembio) = 0.222 / 0.231 = 0.961

Please rate if you are satisfied with the answer.

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