Probability Question On Covid 19. Please help

[Alkaneseries]

The widely used Elisa tests for Covid-19 antibodies have, according to the manufacturer, 100% sensitivity ,i.e. no false negatives, those who have gone through the infection always get a positive test result, and 98.5% specificity (i.e. 1.5% false positives). We assume 1,3% of the population have had a Corona infection.(This is just an assumption. 1,3% of the population of Germany means about a million infections. At the end of April, we have had about 150,000 confirmed cases.) (source: https://www.sueddeutsche.de/gesundheit/corona-testantikoerper-1.4883631, in German) a) Evaluate the probability to have had a Covid infection, if the test is positive. b) Evaluate the probability to have had a Covid infection, if the test is negative. c) Evaluate both probabilities with the assumption of 10% of the population have had the infection.

Hint: Law of Total Probability