Math Puzzle: False Positive
June 2nd, 2009
| Categories: Math Puzzles, Probability
Level of difficulty: highschool
This puzzle is about false positives (False Positive also happens to be the name of the band I play in, but that’s another story). The question itself is straightforward but the result is surprising, at least to those who haven’t seen such results before.
Suppose you’re going to get tested for skin cancer (knock on wood, etc). The test itself is quite good: it has 95% accuracy, meaning it identifies sick people as sick with a probability of 95%, and healthy people as healthy with a probability of 95%. Now, a gross estimate would be that skin cancer affects 1 in 5000. Given that the test says you’re sick, what is the probability that you really are sick? Hint: it’s not 95%.
EDITED, 3/June/2009: a solution has been posted here.
Aha, now this one I know inside out. I’ll hold off though, let someone else give it a try
I hope you have a video explaining this one! Such an important concept.
Thanks for holding off. However I’m going to increase the puzzle posting rate for the near future, so feel free to fire away the moment you know the answer. No movie this time, unfortunately - it takes me about half a day to a day to make one, so I’m saving them for special occasions :).