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 a team of scientists has created a new variant of RT-PCR test which is called as RT-PCR-. This test has improved 100% sensitivity and maintains 70% specificity as before (note the definition of sensitive and specific from Q1). Now answer part (a) - (c) of Q1 for RT-PCR- test.

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