Part 1) Suppose RT-PCR test for detecting whether a person has contracted corona virus is 90% sensitive, meaning that it correctly predicts positive for 90% infected people. Moreover, the same test is 70% specific, meaning that it correctly predicts negative for 70% of noninfected people. Assume that 8% of the population has contracted the virus. (a) What is the probability that a person who tested positive has actually contracted the virus? (b) What is the probability that a person who tested negative has actually contracted the virus? (c) For answers for part (a) and (b), interpret when the test is effective or not effective?

Part 2) Suppose that another team of scientists has improved the original RT-PCR test from Q1 which is called RT-PCR-. This test has improved 90% specificity and maintains 90% sensitivity as in Q1 (note the definition of sensitive and specific from Q1).

Then, answer. part (a)-(c) of Q1 for RT-PCR- test.