Suppose that, when a person, who either contracts Covid-19 virus (C=contracted) and (NC = not contracted) arrives at a test location, the first test will be applied on him/her and will mark them as positive (+) or negative (-) for Covid-19. If the result is positive, the second test will be applied on them later on to see if they have contracted or not contracted Covid-19. Assume that 10% of all tested carry the virus and that the two tests are each 90% accurate, in the sense that P(+ l C) = 0.9 and P( - l NC ) = 0.9 for each test. Also assume that given whether a person carries Covid-19, the two tests outputs are conditionally independent.

1) Find the probability that the person carries the virus, given that the first test marks them as positive.

2) Find the probability that the person carries the virus, given that the both tests mark them as positive.