3 doors, 2 pigs and a Ferrari!

[Aelia Jusa]

This is how I undderstand it, which may help those who are still thinking 50/50.

In the first instance, you have a 33% chance that the door you pick will have the car. Therefore, there is a 66% chance that one of the other two doors will have the car.

With the information you have to start with (that is, one of these three doors has the car), all you can know is that of the two doors you haven't picked both are equally likely to have the car. So the two doors you haven't picked each have a 50% of 66% chance of having the car (i.e., 33% chance each).

Then you are told that one of the doors you haven't picked doesn't have the car. So you now have the information that, of the two doors that together had a 66% chance of having the car, one of them has a 0% of 66% chance of having the car (i.e. 0% chance). Therefore, the other door must have a 100% of 66% chance of having the car (i.e. 66% chance).

So the door you originally picked has a 33% chance, the other two doors together have a 66% chance, and since you know one of the 66% doors is not it, then you should swap because the other one must have a 66% chance of being the right door.

[Encard]

This is very simple, folks...

If you initially pick a pig door, switching after the host eliminates the second incorrect door weill get you the car. You have a 2/3 chance of initially picking a pig door, and thus of getting the car when you switch.

If you inititally pick the car door, switching will get you a pig. You have a 1/3 chance of picking the car, and thus getting a pig if you switch.

If you stay, the numbers are reversed - you have a 2/3 chance of ending up with a pig after the second pig door is eliminated, and a 1/3 chance of ending up with the car.

[The Collective]

Well structured and logical arguments from Aelia Jusa and Legolas - when we take over your puny planet you have been earmarked for elevation from our conquered slave labour force.

[Lanesra]

Originally posted by Q'alooaith: It's two actions, not one. Pick a door(first action) Chance of guessing right 33.33% One Pig Revealed, it is never the door you picked. Door is now an inoproriate choice, so is discarded.

I don't think you understand the question. You pick a door and I open one of the other 2 doors. I can't open the door you picked.

[Aragorn1]

Originally posted by Bozos of Bones: Weren't we all over this before some three weeks? Oh, an in that thread my riddle remains unanswered.

Yep: http://www.ironworksforum.com/ubb/cg...=000973#000002

Here's the diagram I found to help explain it:


The mathematical PROOF is on one of my posts too, but its quite diffcult to understand.

[ 07-27-2005, 07:45 AM: Message edited by: Aragorn1 ]

[Lanesra]

Let's put it like this. If there are a zillion doors and you choose one you must agree that it's unlikely to have a car behind it. Now I start opening doors, when I get to the end there is one door left unopened and the only reason it's unopened is because I know there is a car behind it.

Simple really.

I guess some of you get suprised when every time there is a piece missing in a jigsaw puzzle it's always the last one!

[Cloudbringer]

Why does this thread make me think of Magnum PI? Luau's, ferrari's and crazed people knocking down doors....

So is it a pig or a goat and what if the chooser WANTS the barnyard animal instead of the car? [img]graemlins/biglaugh.gif[/img]

[Mr. Mopery]

Originally posted by Aragorn1: Here's the diagram I found to help explain it: The mathematical PROOF is on one of my posts too, but its quite diffcult to understand.

THAT'S NO PIG. What are you trying to pull???

Now we see truth! Behind the "good" door, what'll there be instead of a Ferrari?

[Iron Greasel]

Whoah! I actually understood that! Thank you, smart people, that one has always troubled me before.

[Timber Loftis]

It's a 50/50 shot either way, so swap or don't swap. Now go peddle your voodoo mathematics elsewhere.