Assume we know the following facts about COVID-19 testing:

95% of infected people test positive. This is called the true positive rate.

0.01% of uninfected people test positive. This is the false positive rate.

Based on population-level statistics in Oregon, we expect that among all people who are tested, 10% are infected.

With this information, please answer the two questions below:

a. John, who lives in Oregon, tests positive. What is the probability that he is infected?

A) 0.999

B) 0.099

C) 0.5

D) 1

b. With all other values remaining the same, what should the false positive rate change to, for John's probability of being infected to change to 0.95?

A) 0.556%

B) 0.056%

C) 0.1%

D) 1%