A small probability correction

[Equations in this post may not look right (or appear at all) in your RSS reader. Go to the original article to see them rendered properly.] This short video appeared in my YouTube feed last week. It’s from Hannah Fry, whom you probably know from her appearances on Numberphile and other STEM-oriented stuff. If you’re in the UK, you’ve may have seen her on the BBC, too. The short presents a classic problem in conditional probability, but the answer she comes up with is wrong. It’s a good estimate, and it’s the same answer I got when I stopped the video and tried to work it out in my head, but it’s still wrong. By just a little bit. Here’s the problem: There’s a disease that affects 1 in 1,000 people. A test for the disease is perfect in one sense but imperfect in another. If you have the disease, the test will return a positive result 100% of the time. If you don’t have the disease, the test will return a negative result 95% of the time but a positive result 5% of the time. If you have…