Ah, these are fun. Probability "paradoxes" that confuse intuition are plenty even without poking at infinity in some way, at least as witnessed by the Monty Hall problem (ok, yes I know this one is trivial to anyone studying probability). It reminds me of the time I spent musing over variants of https://en.m.wikipedia.org/wiki/Two_envelopes_problem . This has at least a common theme in not having a well defined prior distribution.
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