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Notes -
I’m convinced this is easy to explain to pretty much anyone, just by making clear that the fact that you chose gold first makes the double-gold box more likely than the mixed box because coins of the same type are fungible.
Like the Monty hall problem, people who make the mistake do so not (necessarily) because they’re stupid, but because they just haven’t been taught to think carefully about the “given that” aspect of these probability questions.
If you pick a gold coin in box A, you have a 100% chance of getting a second gold. If you pick a gold coin in box B, you have a 0% chance of getting a second gold. (100+0)/2 does indeed equal 50. But the first gold was clearly twice as likely to come from the double-gold bucket as the mixed bucket, which means that the chance of a second gold is obviously also higher.
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