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Double Illusion of Transparency

I had a similar run-in when I tried to go through the Cantor Diagonal Argument with a bunch of gifted 13-year-olds. I thought I had them following right through to the end, but when I came to the conclusion, they cried: "But infinity is infinity!"

Not quite as concrete as Bayesian inference, but it's still a difficult concept. Some of those students would probably never think of that lecture again, and some, after some years of ruminating and/or majoring in math, would finally understand what I was getting at. After having that run-in, I actually switched over to teaching conditional probability (in particular, the Mony Hall problem) as my "fun" math lecture.