Suppose a disease takes place with 0.1% frequency in the population. Now lets say theres blood test which comes back positive with 99% probability if the disease is present (i.e., 99% correct), but 2% correct if not (i.e., 2% false alarm rate).
Determine the conditional probability that someone has the disease, given a positive test result? Hint: you need to be familiar with the Bayes rule and the total probability rule.
The resulting conditional probability is pretty low, which is kind of counter-intuitive. Please given a short explanation.