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You seem to be ignoring that because of the first part, one door is more likely to be right than the other. What you are saying is like saying that "the sky may fall tomorrow, or it may not, therefore both possibilities have an exactly 50/50 chance of happening."

I think the point you are missing here, Batvink, is that there are two different goats. After one door is removed, there are actually three different possibilities:

your pick - the other door
goat A - car
goat b - car
car - either goat

Or another way of explaining it:
Seeing as you want to use this Law of Probability, lets say each door has a 1/3 chance of having the car. Put doors 2 and 3 together and they have 2/3 chance of having the car between them.
So you have one door with one thing behind it, another door with two things behind it.

The host of the show will give you the car if you pick the door with the car behind it, regardless of whether there's also a goat in there. Door 2-and-a-half is twice as likely to have the car behind it as door 1.

Therefore if you pick door 2-and-a-half you have 2/3 chance, and door 1 has 1/3 chance.

Combining the doors is exactly the same as removing one goat, because the goat isn't counted if it's with the car, although you have to count it to work out the probabilities because there are 2 things behind door 2-and-a-half.

Dig?

The best way I figured out how to explain this was to my mate. I'll paste in the exact final dialogue after out discussion.

(10 doors, I secretly choose 5 as the car)
Me: Choose a number between 1 and 10
Him: 3
Me: Ok, it's not 1,2,4,6,7,8,9 or 10. That leaves 3 or 5. Stick or switch?
Him: Ahhhh ... I get you now.



When you have it laid out in front of you like that, it becomes more obvious. They know they have a 1 in 10 chance of getting it right. It's like:

-Lay face down all 52 cards in a pack of cards (know where the ace of spades is)
-Ask them to pick the ace of spades.
-They choose one.
-Then remove all cards except the one they picked first and one other (if its the ace of space (which it has a 51/52 chance of being, seeing they only have a 1/52 chance of picking it right the first time).
-Now stick or swap?

Simple fact is, there is a 1/52 chance of you getting it right the first time. That cannot change. Odds like that can't change. If there is a 1/52 chance of the card being right, it will stay like that, no matter what you do with the other cards because the card they've chosen will still be the same. That means that by the laws of probability, the remaining cards (no matter how many there are) have a 51/52 chance of containing the ace of spades. By removing all the remaining cards except one, you are making that one card a 51/52 chance. It's not as simple as saying that has a 1/52 chance aswell, because remember, you're not taking cards away at random based on probabily. That card is left by the person who knows which card is which. There is no probabilty in their methology.

It's the fact that 3 boxes are used that make it even tougher to get your head round.

also the fact that they're removing one of the GOAT doors is confusing. If they'd just remove One of the remaining doors (without telling you), it'd be 1/3.

They can't do that though because they may remove the car door making it impossible to win.

I think he means if they open any door irrelevent of whats behind it then the two remaining doors have 33% chance each.

Imagine shouting at the TV..SWAP! SWAP!
No one realised in those days that you should swap??? I'm not surprised, the solution is so confusing.

Why keep debating this? Exeat explained it perfectly.

That's the point of a forum : debating.
If everybody would have the same opinion, a forum would be worthless

Yes.. I like Mass Debating!