can you make a tree diagram and show how you got the following answers?

10.47 Assessing the new OraQuick HIV test. In 2012, the U.S. Food and Drug Administration approved the first over-the-counter HIV testing kit, the OraQuick In- Home HIV Test. Example 10.12 told us that the sensitivity and specificity of a diagnostic test are determined experimentally. The OraQuick test was approved based on a study that examined the test results of a sample of 4410 adults from a high-risk population who did not yet know their HIV status. Each person's actual HIV status was later confirmed via several other medical examinations. Here are the findings:44 105 true-positives (HIV and positive test) 8 false-negatives (HIV and negative test) 1 false-positive (no HIV and positive test) 4296 truc-negatives (no HIV and negative test) (a) What is the sensitivity, P (positive test HIV), of OraQuick? This represents the fraction of all HIV cases who received a positive test result. Use the counts in the table of findings to obtain your answer. (b) What is the specificity, P (negative test no HIV), of OraQuick? This represents the fraction of all individuals with no HIV who received a negative test result. (e) Now use the study findings to find the approximate rate of HIV in this high-risk population. What is the positive predictive value of OraQuick, P (HIV positive test), in this high-risk population? (d) Explain in your own words why the positive predictive value of this test would be different for a population with a different rate of HIV, whereas the test's sensitivity and specificity would remain the same. Q: Click to display the answer to this question, Hide Answer (a) 0.9292. (b) 0.9998. (c) 0.0256 and 0.9906, respectively. (d) PPV depends on the rate of HIV in the population screened because it influences how many true-positives and false-positives we would get. But the sensitivity and the specificity are properties of the OraQuick test that depend only on chemistry and manufacturing