A nice probability problem to talk thorugh with kids

Saw this problem from the 2012 AMC 10 b tonight:

Screen Shot 2016-01-28 at 7.19.10 PM

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:



2 Comments so far. Leave a comment below.
  1. 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.

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