6:44 Outlook 1 of 3 Probability Lab Marshall University STA 150L Conditional Probability Lab - Applied Problem The Human Immunodeficiency Virus (HIV) causes AIDS. A person who has been infected with HIV is described as HIV positive; a person who has not been infected is HIV negative. One commonly used test of HIV is a enzyme immunoassay test. According to Wikipedia, The specificity rate given here for the inexpensive enzyme immunoassay screening tests indicates that, in 1,000 HIV test results of healthy individuals, about 15 of these results will be a false positive. ... The sensitivity rating, likewise, indicates that, in 1,000 test results of HIV infected people, 3 will actually be a false negative result According to the Centers for Disease Control (CDC) 2 approximately 1.1 million citizens of the U.S. were HIV positive in 2016. The U.S. population in 2016 was about 323 million. 1. Estimate the percentage of the U.S. citizens in 2016 who were HIV positive, based on the data above. We will treat this as the probability that a randomly selected U.S. citizen is HIV positive. 2. What is the probability that an HIV positive individual will test negative under the enzyme immunoassay test described by the quote above? 3. What is the probability that an HIV negative individual will test positive under the enzyme immunoassay test described by the quote above? 4. Use your answers to the previous parts to fill in the following table. Assume that we begin with a population of 1,000,000 randomly selected U.S. citizens. Fill in the row totals first and then fill in each row. Test positive Test negative Row total HIV positive HIV negative Column total 1,000,000 http://en.wikipedia.org/wiki/Diagnosis_of_HIV/AIDS. Their data is based on Chou R, Huffman LH, Fu R, Smits AK, Korthuis PT (July 2005). "Screening for HIV: a review of the evidence for the U.S. Preventive Services Task Force". Ann. Intern. Med. 143 (1): 55-73, https://annals.org/aim/fullarticle/718529/ screening-hiv-review-evidence-u-s-preventive-services-task-force. 2 AIDS.gov: U.S. Statistics, http://www.aids.gov/hiv-aids-basics/hiv-aids-101/statistics/ 1 Conditional Probability Lab Marshall University STA 150L 5. Based on our table, what is the probability that a randomly selected person who tests negative under the enzyme immunoassay test is HIV positive? Note: this is a conditional probability. 6. Based on our table, what is the probability that a randomly selected person who tests positive under the enzyme immunoassay test is HIV positive? Note: this is a conditional probability. coursehero.com