Part 1. Imagine that a new test for COVID-19 has been developed that is y% sensitive (the True Positive Rate), and z% specific (the True Negative Rate). Assume that the prevalence of COVID-19 in the population that the the test will be used in is 15%. Choose numerical values for y and z (not x), and then calculate the test's precision and recall. Provide your step-by-step calculations, and your final four numerical quantities, y, z, precision, and recall.

A tip: this Wikipedia page about Precision and Recall(Links to an external site.) provides a nice summary of different kinds of binary classifier metrics.

Part 2. Using your values and the prevalence of COVID-19, estimate the probability that an individual who gets a positive for COVID-19 from this test actually has COVID-19. (Hint: Use Bayes Theorem, and also think about the hint that was provided in Sync-3: there are only two ways a positive test result can occur.)