Assume you are tested for a disease called C, a medical condition that afflicts 0.1% of the population. The test result is positive, i.e., the test claims that you have the disease. You immediately ask for a second, independent test to be performed. Suppose that these tests are 99.9% accurate and their results are independent of each other. Here we take accuracy to mean that the probability that the test result is positive if you have the disease (the test's sensitivity) is 99.9% and the probability that the test result is negative if you do not have the disease (the test's specificity or true negative rate) is also 99.9%. Using a simulation study, or otherwise, answer the following questions:

1. What is the probability that you have C if the first test comes back positive?

2. What is the probability that you have C if the second test comes back positive too?

3. What is the probability that you have C if the second test comes back negative?

4. If C is a disease that has to be reported to the authorities, which result would you report: the result from the first test or the result from the second test?