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As to
JD's objections, I agree that this is not a real life problem. But I
think it could be worded well enough so that the exercise is valid.
Take the dealer's comments out of the scenario and instead let it be
a computer game (guaranteed to be programmed fairly). You are dealt
the two cards face down. There is a button you can click to ask for a
hint. The computer can respond:
1. no hints today -- I am tired
2. you have at least one ace -- I don't know what suit it is
3. you have at least one ace and it is the ace of spades.
Then I think the exercise is intact and it shows the non-intuitive
ways that additional information can affect probability.