Assumed that 2% of the population in a city is infected by COVID19. It is also assumed that from those who are infected took the PCR swab test, there is a 99% chance that the test will return a "positive" reading.Keep in mind that these tests are not perfect. Even if the suspect did not have COVID19, there is some probability that the test will return a positive. Let's suppose that, given that a people did not infected by COVID19, there is still a 3% chance that the swab test will return a positive (and the suspect has to be quarantined).

A. Use a tree diagram to list the sample space for showing all possible outcomes after selecting a suspect (who either had COVID19 or did not) and then testing (and the test will be either positive or negative).

B. Calculate the probability that the suspect did not have COVID19.

C. Calculate the probability that the suspect had test positive, given that he did not have COVID19.

D. What is the probability that a randomly chosen suspect will be COVID19-free and will still test positive for COVID-19?

E. Suppose the suspect had test negative. What is the probability that he had COVID19?