More than 1.5 million tests for the COVID virus were performed each day in the United States during the COVID-19 pandemic in 2021. Many employers, schools, and government agencies required negative COVID-19 tests before allowing people on their premises. Suppose that for a particular COVID-19 test, the probability of a false negative (meaning that a person who is actually infected with the COVID-19 virus tests negative for the virus) is 0.1, and that the test always gives a negative result for someone who is not infected with COVID-19. Suppose also the probability that a randomly selected person is infected with COVID-19 is 0.05. Answer the following questions.

a. What is the probability that someone who tests negative for the COVID-19 virus actually has COVID-19?

b. Suppose that a large school system states that 2,500 of its students have reported a negative COVID-19 test. Of these 2,500 students who tested negative, how many would you expect to have COVID-19?

c. Suppose the incidence of COVID-19 is actually considerably higher and the probability of any randomly selected person having COVID-19 is 0.20. What is the probability in this case that someone who tests negative for the COVID-19 virus actually has COVID-19? Explain this change from part (a).