Consider two medical tests, A and B, for a virus. Test A is 95%
effective at recognizing the virus when it is present, but has a 10%
false positive rate (indicating that the virus is present, when it is
not). Test B is 90% effective at recognizing the virus, but has a 5%
false positive rate. The two tests use independent methods of
identifying the virus. The virus is carried by 1% of all people. Say
that a person is tested for the virus using only one of the tests, and
that test comes back positive for carrying the virus. Which test
returning positive is more indicative of someone really carrying the
virus? Justify your answer mathematically.

Consider two medical tests, A and B, for a virus. Test A is 95%
effective at recognizing the virus when it is present, but has a 10%
false positive rate (indicating that the virus is present, when it is
not). Test B is 90% effective at recognizing the virus, but has a 5%
false positive rate. The two tests use independent methods of
identifying the virus. The virus is carried by 1% of all people. Say
that a person is tested for the virus using only one of the tests, and
that test comes back positive for carrying the virus. Which test
returning positive is more indicative of someone really carrying the
virus? Justify your answer mathematically.