I have the following problem:
Patients are tested for a particular disease. For each patient, the result of the test (infected or not) is correct with the probability 0.8. Suppose that 20% of the patients are infected. What is the probability that a given patient is indeed infected if his/her test result shows ‘infected’?
Feels that I need to use the Bayes theorem, but the information about test results confuses me a bit. What is the right solution for this problem?