A hospital designed a new test testing Covid-19. Suppose when the test result is positive the patient is truly infected with Covid-19 at a 98% chance, and when the test result is negative, the chance that the patient is infected is 3%. Now assume only 0.1% of people are infected with Covid-19.

a.Based on your intuition, if one person was tested positive, what is the chance that he is really sick?

b.Calculate the probability that person is sick when he is tested negative i.e. Pr(infected with Covid-19|negative test result).

c.Calculate the probability that person in question a. is really sick i.e. Pr(infected with Covid-19|positive test result).