The BinaxNOW COVID-19 antigen test is sold as an in-home test. Pollack et al. (2021) estimate that among asymptomatic adults, the test has a 70.2% sensitivity and 99.6% specificity. Assume for this question that 8% of people who use this test actually have the disease.

a) Draw a tree diagram representing this situation.

b) What proportion of tests given to asymptomatic people will be true positives?

c) What proportion of tests given to asymptomatic people will be true negatives?

d) What is the probability that an asymptomatic person who tests positive truly does have COVID-19? "Fun" fact: this probability is called the positive predictive value.

e) What is the probability that an asymptomatic person who tests negative truly does not have COVID-19? This quantity is called the negative predictive value.