The ELISA tests whether a patient has contracted HIV. The ELISA is said to be positive if it indicates that HIV is present in a blood sample, and the ELISA is said to be negative if it does not indicate that HIV is present in a blood sample. Instead of directly measuring the presence of HIV, the ELISA measures levels of antibodies in the blood that should be elevated if HIV is present. Because of variability in antibody levels among human patients, the ELISA does not always indicate the correct result. The test gives a positive result 8 percent of the time for people who do not have HIV. The test gives a negative result 1 percent of the time for people who do have HIV. According to U.S. Census Bureau approximately 14 percent of the population in the United States is living with HIV.

Part (a): Draw a tree diagram for this chance process.

Part (b): If a person is selected at random, what is the probability they would test positive for HIV?

Part (c): Given that a person selected at random tests positive for HIV, what is the probability they do not have HIV?