arpruss
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arpruss has not written any posts yet.
arpruss has not written any posts yet.
Thanks for all the comments. For those who are drawn to not changing the probability all the way through the story--which, I agree, is the intuitively right answer--I recommend looking at this variant where sticking to your guns leads to incoherent probabilities.
It's only if the sets are countable that we can probabilistically predict ahead of time that there is a pairing. To get the existence of a pairing, we need to know that the cardinality of those who rolled six is equal to the cardinality of those who didn't. It is a consequence of the Law of Large Numbers (or can be easily proved directly) that there are infinitely many sixes and infinitely many non-sixes. And any two infinite subsets of a countable set have the same cardinality. But in the uncountable case, while we can still conclude that there are there are infinitely many sixes and infinitely many... (read more)