We want to analyze performance and cost of a COVID-19 screening tests for a university campus. The system is based on two tests: 1] a rapid do-it-yourself test, that has a probability of error of 17%% and costs 800 tenge; and 2) a more reliable PCR test, that has a probability of error of 5% and costs 7700 tenge. We refer as probability of error as either false negative (the student has COVID but the test detects negative) or as false positive (the student does not have COVID but the test shows positive). Tests are arranged in this way, on a 2-week basis with 5 test days: - Each student makes a rapid test every 3 days (day 3, 6, 9, 12 of the period). - If the rapid test shows negative, the student will perform the next test as planned. - If the rapid test shows positive, the student will make a PCR test immediately after. If the PCR test shows negative, the student will perform the next test as planned. - On the 14 th day, the student will make a PCR test. If the PCR is negative, the student will proceed to the next 2-week test period, as planned. - If any PCR shows positive (whether performed after the rapid test, or at the 14th day as by the test plan), that is considered as a positive detection, and the student will be then treated. At every test day, the whole campus population will get tested. For simplicity, we know that the campus population is always 1500 students, and we know that at any test day 25 students are sick with COVID-19. So, at each 3 rd, 6 th, 9 th, 12 th, and 14 the day of the 2-week test period, 25 students are sick and 1475 students are not sick with COVID-19. Answer the following questions: aj If we know that a student is sick with COVID-19 on day 2 of the 2-week period, what is the probability that he will test negative until day &? b] We define a success if: a student who is sick gets tested positive on the first test date, or a student who is not sick gets tested negative on the first test date. What is the expected value of the success probability? () What is the expected cost over 1 year (52 weeks) of this test system