Re: [Phys-l] probability problem

[John Mallinckrodt <ajm@csupomona.edu>]

On Jun 28, 2010, at 4:39 PM, Stefan Jeglinski wrote:

> Correct me if I'm wrong but I want to understand your point:
>
> > 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.
>
> You're saying that in "real life" Monty might have unstated  
> motivations, no?

Right.  If the problem statement included a specification that Monty  
was required to show you a goat, then you could be certain that your  
chance of success is doubled by switching.

> > 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.
>
> Likewise the dealer in saying "wow"?

Yes.  I meant the dealer.

> I take it your point is that neither issue changes the problems, as
> stated, but that in "real life" there may be other considerations to
> think about?

I wouldn't say that.  Indeed, I think the card problem as stated  
makes it clear that it *is* about real life.  If the cases had been  
laid out passively as,

"You obtain the following additional information:

1) No additional information

2) The hand includes at least one ace

3) The hand includes the ace of spades"

then I wouldn't be motivated to wonder about the dealer's motivations  
for saying what he or she did.