lished a report on the 3) HIV Testing: In July 2005, the journal Annals of Inter

Question

lished a report on the 3) HIV Testing: In July 2005, the journal Annals of Internal Medicine pub reliability of HIV testing. Results of a large study suggested that amo 99.7% of the tests were (correctly) positive, while for people without HIV 98,5 were (correctly) negative. A clinic serving an at-risk population offers free HIV t believing that 15% of the patients may actually carry HIV. ng people with HIv % of the tests testing, (Hint: a tree diagram may be helpful) a) What is the probability that a person will test positive for HIV? b) What is the probability that a person will test negative for HIV? c) What is the probability that a person testing negative is truly free of HIV?

Explanation / Answer

P(actually carry HIV) = 0.15

P(do not carry HIV) = 1 - 0.15 = 0.85

P(tests positive | have HIV) = 0.997

P(tests negative | have HIV) = 1 - 0.997 = 0.003

P(tests negative | doesn't have HIV) = 0.985

P(tests positive | doesn't have HIV) = 1 - 0.985 = 0.015

a) P(tests positive) = P(tests positive | have HIV) * P(have HIV) + P(tests positive | doesn't have HIV) * P(doesn't have HIV)

                              = 0.997 * 0.15 + 0.015 * 0.85

                              = 0.1623

b) P(test negative) = 1 - P(tests negative) = 1 - 0.1623 = 0.8377

c) P(doesn't have HIV | tests negative) = P(tests negative | doesn't have HIV) * P(doesn't have HIV) / P(tests negative)

                                                               = 0.985 * 0.85 / 0.8377

                                                               = 0.9995

Related Questions

Navigate

• Browse (All)
• Browse L
• Subjects

---

---

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