Question

3. It is estimated that 2% of the members of a certain population are infected with Hepatitis C virus. A diagnostic test for detecting Hepatitis C yields 4% false positive and 5% false negative results. (a) Find the probability that a person randomly chosen from this popu- lation has a positive result of the diagnostic test for Hepatitis C. (b) Find the probability that a random person who has a positive result of the diagnostic test, actually has Hepatitis C
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Answer #1

3.

A) required probability = 0.02*0.96 + 0.98*0.04 = 0.0584

B) required probability =

(probability of true positive detection for hepatitis c patient) / (probability of actually having  hepatitis c )

= (0.02*0.96) / 0.02 = 0.96

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