Imagine a disease occurs with 01 frequency in the population

Imagine a disease occurs with 0.1% frequency in the population. Now lets say theres a blood test that 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).

(Q.1, 15 points) What is 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.

(Q.2, 5 points) The resulting conditional probability is pretty low, which is kind of counter-intuitive. Please given a short explanation.

Solution

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