2 Blood donors are usually screened for HIV, both for the safety of the blood su

Question

2 Blood donors are usually screened for HIV, both for the safety of the blood supply and for the benefit of the donor. The test, called an ELISA, tests positive 97.5% of the time if the donor actually has HIV. If the donor does not have HIV, the ELISA test correctly indicates that the person does not have the disease 92.6% of the time. About 0.2% of college students have HIV. After a blood drive at a college, the lab calls and tells a student that the test has indicated he has HIV. Use what you have learned in this lesson to determine the probability that the student actually has HIV. Because the prevalence of HIV is so small, it may be better to use 100,000 as your total population. A B Considering the answers to questions 1 and 2, should you be more concerned about a positive test for a rare disease or a common disease? Explain your answer.

Explanation / Answer

Solution-

Let us denote the events as-

D - HIV disease is actually there

N- HIV is not present

P- Test comes positive

Given the probabilities that-

P(D) = 0.002 and P(N) = 1- P(D) = 0.998

P(P|D) = 0.975 and P(P|N) = 1 - 0.926 = 0.074

(A) We will calculate the probability that he actually has HIV when he is tested positive -

P(D|P) = P(D) * P(P|D) / [ P(D) * P(P|D) + P(N) * P(P|N) ] { using bayes theorem}

= 0.002 * 0.975 / (0.002*0.975 + 0.998 * 0.074 )

= 0.02573

(B) Question 1 has not been provided here, so wont be able to answer this question!

Thanks!

Related Questions

Navigate

• Browse (All)
• Browse 2
• Subjects

---

---

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