According to official estimates of a country, 1% of the population has infected Covid. Suppose one resident in this country took two Covid tests, A and B.

Each individual test has a 1% type-I error and 1% type-II error. That is:

1% of residents who have Covid is tested (falsely) negative;

1% of residents who have no Covid is tested (falsely) positive.

a.)If this resident gets a positive result from test A, what is the probability that he does have Covid? (For this part a, you can ignore test B).

b.)Now consider both tests. If both tests A and B are positive, what is the probability that this resident has Covid?

c.) When answering the above questions, do you need to make any assumption(s)? If so, state the assumption(s) clearly.