Problem 2: COVID-19 Testing (calculating posterior probabilities)

There are many tests for COVID-19 available in the market (see for example the following website: https://www.centerforhealthsecurity.org/resources/COVID-19/serology/Serology-based-tests-for-COVID-19.html). Consider one of those tests with sensitivity 93.8% and specificity 95.6%. Suppose you are planning to use this test on random persons in two countries. In one, you believe 2% of population is infected. In the other, you believe 50% of population is infected.

Determine for each country the probability that a person is infected given that the test is positive and the probability that the person is not infected given that the test is negative.