Do I have the disease? (Solution)

Classic bayes-rule question. Instead of using the formula, let’s solve it using an example.

Let’s start with a population of 1000 people. 2% of people have the disease, so that’s 20 people.

Yes Disease	No Disease
20	980

If everyone took the test, 95% of the 20 people with the disease would be positive; that’s 19 people. 10% of the 980 people without the disease would be positive; that’s 98 people.

	Yes Disease	No Disease	Total
Test Positive	19	98	117
Test Negative	1	882	883
Total	20	980	1000

You take the test and you’re positive. Given that information, we now only care about the “Test Positive” row. In that row, 19 out of a total of 117 people have the disease. So the chance you have it is \(19/117 \approx 0.16%\).