Saw this problem from the 2012 AMC 10 b tonight:
you can find the problem (and the entire test) here:
The 2012 AMC 10b on Art of Problem Solving’s site
It looked like a neat problem to talk through with both of the boys. I started with my older son first:
Next up was my younger son who had some fun with it, too:
Mike's Math Page 
Gerd Gigerenzer has written several nice books related to this type of problem, particularly thinking about the use of probability and statistics in medicine/health sciences.
Some follow-up explorations/discussions:
(1) what are the costs of testing?
(2) what actions can be taken once test results are known? What are the costs, benefits, and probabilities?
(3) Should people in the general population get the test or not?
(4) if someone gets a positive result, how should that be communicated to them?
(5) If someone gets a negative result, how should that be communicated to them?
I’ve long felt that this was a very important topic. For the last 10 years, I have used a version of this as a case interview question when hiring.
Yeah – the famousness / importance of this type of problem is why I talked about it with both kids.