Problem 1) A test is used to determine whether a person is infected by a virus.

Question

Problem 1) A test is used to determine whether a person is infected by a virus. The probability that the test correctly identifies someone with the virus infection as positive is 0.8, and the probability that the test incorrectly identifies someone without the virus infection as positive is 0.05. The probability of virus infection in the general population is 0.005 (a) (8 points) A person takes the test and the result is positive. What is the probalbility that the person has the virus infection? (Round your answer to four decimal places)

Explanation / Answer

P(P|V) = 0.8 and P(P'|V) = 0.2
P(P|V') = 0.05 and P(P'|V') = 0.95
P(V) = 0.005 and P(V') = 0.995

P(V|P) = P(P|V)*P(V)/(P(P|V)*P(V) + P(P|V')*P(V'))

P(V|P) = 0.8*0.005/(0.8*0.005 + 0.05*0.995) = 0.0744

Required probability = 0.0744

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.