Imagine there has been an outbreak of a rare disease in your hometown. Only 1 out of every 200 people is infected and there is a test that can detect if you are infected (or not) with an accuracy of 95%. You take the test and the result is positive, indicating that you have the disease.
What is the probability that you are infected?
Intuitively, the answer to this question seems to be 95%. But if you are familiar with Bayes’ theorem (or if you read the title of this blogpost) you might know that the probability of having the disease is much lower than that. It’s only 8.7% to be exact.
How can this be? Continue reading