Cellex make an FDA-approved antibody test for Covid 19 (https://www.ncbiotech.org/news/cellexcleared-market-antibody-test-covid-19). It's my understanding that the sensitivity of the test is 93.8% and that the specificity is 95.6%. A positive test is supposed to indicate that you have had Covid 19 and that as a result you are now immune and safe to return to work.

a) If 1% (3.3 million people) of the population has been infected by Covid 19, what is P(+ Test)?

b) What is P(Covid 19 | + Test)?

c) If 100 people test positive with the antibody test, how many people will be allowed to return to work even though they have not had Covid 19 and are not immune?