Re: [Phys-l] probability problem

[John Mallinckrodt <ajm@csupomona.edu>]

Beyond the mathematical analysis, there is, unfortunately another  
dimension that is best illustrated by the Monty Hall problem:  
(Recap:  Monty allows you to pick one of three curtains behind one of  
which is a DeTomaso Mongusta Ghia and behind the other two of which  
are goats.  After you pick, he shows you a goat behind one of the two  
curtains that you didn't pick and then gives you the chance to switch  
your choice to the other remaining curtain.)

The standard analysis of the Monty Hall problem makes clear that you  
are twice as likely to win the car if you DO switch, but that  
analysis ignores the significant possibility that Monty might only  
show you the goat and allow you the opportunity to switch if you have  
already chosen the curtain with the car behind it.

In this case, it seems to me that the probability of having two aces  
in case 3 is likely to be significantly lower than the standard  
analysis would suggest simply because it would seem odd for the  
observer to be more surprised by the appearance of the ace of spades  
than by the appearance of two aces--i.e., the simple fact that the  
observer said "Wow" would lead me to believe that it is *very*  
unlikely that I have two aces.

John Mallinckrodt
Cal Poly Pomona

On Jun 28, 2010, at 6:35 AM, Carl Mungan wrote:

> 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?