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[Phys-l] probability problem



The following problem comes out of Boas. I have a solution on my website. From time to time, someone will email me and say my solution is nonsense. In any case, it's a cute problem:

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You're sitting across from a dealer. He shuffles a single deck of cards and deals you two cards face down. He then looks at them without showing them to you. Consider the following three distinct scenarios:

1. He tells you nothing.
2. He tells you, "You've got at least one ace."
3. He says, "Wow, you've got the ace of spades."

For each of these three scenarios, what is the probability that if you now turn over the two cards you'll find that you've got two aces? IOW, what odds would you take to bet on it?

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The most common disagreement is about scenario 2 vs 3. You folks are pretty smart, so I won't spoil anyone's fun by giving away the possible solutions at the moment.

I think the problem relates to the idea that entropy is connected with what we know about a system and not just about the physical state of the system. -Carl
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Carl E Mungan, Assoc Prof of Physics 410-293-6680 (O) -3729 (F)
Naval Academy Stop 9c, 572C Holloway Rd, Annapolis MD 21402-1363
mailto:mungan@usna.edu http://usna.edu/Users/physics/mungan/