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Carey Carlan

(Don Pearce) wrote in
:

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

"Bill Graham" wrote in message
om
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.