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Re: [Phys-l] probability problem



Spoiler warning: Don't page down to the end unless you want to see a
solution!!

-----Original Message-----
From: phys-l-bounces@carnot.physics.buffalo.edu
[mailto:phys-l-bounces@carnot.physics.buffalo.edu] On Behalf Of Carl Mungan
Sent: Monday, June 28, 2010 9:35 AM
To: phys-l@carnot.physics.buffalo.edu
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.


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1 is straightforward: (4/52)x(3/51)


3 works out for me in the following way: 1x3/51
The argument here (from me) is that the probability of the first ace is 1

But that would mean that the solution to 2 is the same as 3?

Is it possible that your solution is for the situation BEFORE the cards are
dealt, rather than after?
What am I overlooking?