1) Imagine that the sensitivity for a COVID-19 test was 0.7, the specificity was 0.85, and the unconditional probability of a patient having the disease was 0.04. If such a patient tests positive, letp be the probability that they have the disease.

Which of the following seems most representative of the probabilities that we use when we apply Bayes' rule in calculatingp?

a) p=high probability/high probability+low probability

b) p=low probability/low probability+high probability

2) The false positive rate, P(+|N), for a test is given as 0.04. What is the specificity for this test?

3) If P(+|D) = 0.1 for some test, what is its sensitivity?

4) If he sees a wolf, a boy will cry wolf with probability 0.8. If he does not see a wolf, the boy will cry wolf anyway with probability 0.4. If the probability that there is a wolf would otherwise be 0.25, what is the probability that there really is a wolf when the boy crys wolf?