# 6 – SL NB 05 Q False Positives V1 V2

Now, let’s look at an interesting application of Bayes Theorem. Let’s say we’re not feeling very well and we go to the doctor, the doctor says there’s a terrible disease going on, I’ll administer a test for you. Moreover, she says that the test has 99 percent accuracy. More specifically, she says that for every 100 patients that are sick, the test correctly diagnosis 99 of them and for every 100 patients that are healthy, the test correctly diagnosis 99 of them. If we want to be tactical, these are actually called sensitivity and specificity. Then while we’re waiting for our test, we researched the Internet and find that on average, one of every 10,000 people suffers from the disease. The next day the doctor calls with terrible news. She says that we have tested positive for the disease, so now we’re panicking. But before panicking, let’s turn to math and actually calculate what is the probability of being sick. So here’s a quiz. Given the two pieces of information that the test has 99 percent accuracy, and that one out of every 10,000 people have the disease, what do you think the probability is that we’re sick? Is it from 0-20 percent, from 20-40, 40-60, 60-80, or 80-100? Take your guess and enter it below.