On Sun, 15 May 2011 12:14:44 GMT, Carey Carlan
wrote:

(Don Pearce) wrote in
:

On Fri, 13 May 2011 16:05:33 GMT, Carey Carlan
wrote:

(Don Pearce) wrote in
:

On Fri, 13 May 2011 08:09:11 -0400, "Arny Krueger"
wrote:

"Bill Graham" wrote in message
news:t_ydnZKHN4u_QlHQnZ2dnUVZ5rWdnZ2d@giganew s.com
Soundhaspriority wrote:
"Suppose you're on a game show, and you're given the
choice of three doors: Behind one door is a car; behind
the others, goats. You pick a door, say No. 1, and the
host, who knows what's behind the doors, opens another
door, say No. 3, which has a goat. He then says to you,
"Do you want to pick door No. 2?" Is it to your
advantage to switch your choice?" The above is a famous problem.
I've left out the
attribution to give you a few minutes (or forever, if
you want) to enjoy it. Bob Morein
(310) 237-6511

When you pick door #1 you only have a 1/3 chance of
winning. But after you see that there is a goat behind
door #3, your chance of winning is 1/2, so I would change
doors and pick door #2. But I don't really know
why....It's just gambler's instinct with me.

After you know there is a goat behind door #3 and are given a
chance to guess again, there is a 50% chance the car is behind door
#1 and a 50% chance the car if behind door #2. Change your choice
or not, you have a 50% chance of being right.


Lets make it ten doors. You pick one, and get a one in ten chance of
being right. That means that the chances are 90% that the car is
behind one of the 9 doors you did not pick. You know for certain
that at least eight of those doors conceal a goat, so when eight
goats are revealed, you have no new information. The chances are 90%
that the car is behind one of the nine - only now there is only one
remaining to open.

One vital fact here is that the person doing the revealing knows the
contents of the doors and chooses to reveal only goats. Had he been
guessing too, and just happened to reveal only goats, then yes, you
would be down to 50/50.

Alternate:

You walk in with 8 doors already open revealing 8 goats.
The car is behind one of the two remaining doors.
Convince me that your odds are not 50% to find the car.

Why? That isn't what happens. Read again and try to follow,
particularly the last part, which is the vital proviso.

Why? Because at the point of the final decision, that's the situation.
How do the preceding 8 steps affect the final step?

That isn't the final situation. I will take this a step at a time.

There are three doors - one with a car, two with goats

I choose one. I have a 1 in 3 chance of being right

That means there is a 2 in 3 chance of the car being in the other two

I know for a fact that at least one of the other two is a goat.

That does not change the odds - it is still 2 in 3 that the car is in
one of those

The host shows me one of the two - one he knows to contain a goat.

This is not new information, I knew there was a goat there, I still
know there was a goat there.

The odds are still 2 in 3 that the car is in one of those two doors.

But now those 2 in 3 odds have been concentrated into the one
remaining door of the two, which I will open because that is better
than the 1 in 3 chance of it being my first choice.

d