Oh boy. I sense a Monty-Hall, Marilyn vos Savant argument in the making, especially after having read your solution to (ii).
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As a species, we are forever sticking our fingers into the electric socket of the Universe to see what'll happen next. It's a trait that'll either save us or kill us, but by god it's what makes us human beings. I'd rather be in the company of people who look at Mars than people who contemplate humanity's navel -- other worlds are better than fluff. ~~Sir Terence David John Pratchett
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________________________________
From: Carl Mungan <mungan@usna.edu>
To: phys-l@carnot.physics.buffalo.edu
Sent: Mon, June 28, 2010 7:35:17 AM
Subject: [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:
---
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?
---
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
--
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.eduhttp://usna.edu/Users/physics/mungan/
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