You test 1,000 people for cancer. Of the people tested, only 10 actually have cancer. If the person has cancer, there’s a 90% chance that the test will catch it. It will also claim that 1% of healthy people have cancer.
This means that of the 990 healthy people, 9 will get marked as having cancer. It also means that of the 10 ill people, only 9 of them will be noticed. So your odds of actually having cancer, given a positive test result, are only 50⁄50.
I mostly teach this to people who can follow the actual math without blinking, but I’ve found it’s the fastest way to give a very basic explanation of what Bayes means. It’s a specific, concrete example, and it’s also one that feels intuitively useful—you’ve now learned about false positives and false negatives, and how this affects the meaning of actual results.
From there, you can go in to the math, but I’ve found most people who are bad at math can still work it out this way, and most people who are good at math can quickly derive the formulas from the example :)
I’d probably go in to some cool examples of what else it’s been used for, possibly with worked examples if you have the time − 3 minutes is probably a bit short for anything beyond a single concrete example and a few points of why it’s cool (being used to locate nuclear submarines in WW2, breaking the Enigma code, etc. :))
Possibly a handout with a few fun / cool problems in case kids want to practice, and maybe some pointers towards literate on the subject, but I suspect a pre-college audience won’t generally be receptive to such a thing. You’re probably better off just hooking their interest and trusting that the ones who find it cool will have the sense to look it up on Google :)
You test 1,000 people for cancer. Of the people tested, only 10 actually have cancer. If the person has cancer, there’s a 90% chance that the test will catch it. It will also claim that 1% of healthy people have cancer.
This means that of the 990 healthy people, 9 will get marked as having cancer. It also means that of the 10 ill people, only 9 of them will be noticed. So your odds of actually having cancer, given a positive test result, are only 50⁄50.
I mostly teach this to people who can follow the actual math without blinking, but I’ve found it’s the fastest way to give a very basic explanation of what Bayes means. It’s a specific, concrete example, and it’s also one that feels intuitively useful—you’ve now learned about false positives and false negatives, and how this affects the meaning of actual results.
From there, you can go in to the math, but I’ve found most people who are bad at math can still work it out this way, and most people who are good at math can quickly derive the formulas from the example :)
I’d probably go in to some cool examples of what else it’s been used for, possibly with worked examples if you have the time − 3 minutes is probably a bit short for anything beyond a single concrete example and a few points of why it’s cool (being used to locate nuclear submarines in WW2, breaking the Enigma code, etc. :))
Possibly a handout with a few fun / cool problems in case kids want to practice, and maybe some pointers towards literate on the subject, but I suspect a pre-college audience won’t generally be receptive to such a thing. You’re probably better off just hooking their interest and trusting that the ones who find it cool will have the sense to look it up on Google :)