**Question **# 2. A diagnostic test for Disease X has just been released by BigPharmaCorp. It has a sensitivity of 0.8 and a specificity of 0.9. a. Alice lives in a county where the local prevalence of Disease X is 0.1. She takes the diagnostic test and tests positive for the disease. What is the probability that she truly has Disease X? b. Bob lives in a county where the local prevalence of Disease X is 0.65. He takes the diagnostic test and tests positive for the disease. What is the probability that he truly has Disease X? c. Compare the answers you got from parts a and b. Are you surprised?! (No wrong answers). Disease X is a seasonal disease that people usually get sick with in the winter, so everyone in the country takes a diagnostic test once a year before the winter holidays. BigPharaCorp tells the federal government that they can improve the sensitivity of the test to 0.95 if they provide $30 million of research funding (specificity would stay the same). The expected prevalence of Disease X nationally is 0.2 this year (with a total national population of 100 million people). d. How many individuals, in expectation, would test positive with the test if the investment was not made? e. How many individuals, in expectation, would test positive with the test if the investment was made? Assume everyone who tests positive is given a treatment that immediately treats the disease(for free). Treating someone who is not sick does not harm them. Assume QALYS forsomeone without the disease is 1 and for someone with the disease is 0.8 for that year. f. Assuming the government is only interested in the QALYs gained in the next year, is the investment worth it given a willingness-to-pay value of$100,000/QALY gained? (Assume no need for discounting or half-cycle correction).