Puzzle: The Monty Hall Problem

In the game show Let's Make a Deal, there are 3 doors, behind only one of which there is a prize. You pick a door and then one of the remaining two doors is opened; one of the two remaining doors must be empty and this is the door that is opened (they could both be empty). So now there are two unopened doors. You are then given the option of keeping your original choice, or you can switch to the remaining unopened door.
Does it matter whether or not you switch? Do it change the likelihood of you winning?

Category:

Education

Tags:

• math
• monty
• hall
• let's
• make
• deal
• door
• problem

[DementedlyHappy]

Here's what wikipedia has to say (and I paraphrase):

Imagine the same set up, but with 1000 doors instead of three. After picking a door, Monty then opens up 998 of the remaining doors, revealing them all to be duds. So now there are two doors to choose from. It would seem ludicrous to assume that you picked the right door on your first try (a 1/1000 chance) when there was a 999/1000 chance that it was in the other doors, a probability that is now represented by a single door.

[itsgot2beME]

Here's a simplified explanation: you pretty much want to pick the empty door as your first choice. If you select an empty door, monty hall will then reveal the other empty door, thus when you're offered to switch your selection, you will obviously be picking the door with a prize. So then, what are the chances of you originally picking an empty door in the beginning? 2/3.

[Natenator77]

@DementedlyHappy I realise what you are saying here, but it seems like a massive exaggeration. I don't mean to sound like a jerk, please understand that. In the original problem its 1/3 doors. In your explanation (which is obviously helpful) it would actually have been a choice of 333.3333 doors of 1000 in the beginning and then Monty would open another 333 empty doors and you would have the option of keeping the original 333.3333 or the remaining 333.3333 XD

[REDTEAM22003]

Monty Hall need to learn math

[eajoseph217]

@DementedlyHappy Sam Harris explained this in the 'Moral Landscape" video :)

[DementedlyHappy]

@mumiscrunk That's good stuff. I'll refer skeptics there now.

[DarklightALBANIA]

Just saw the movie 21 that explained this problem with percentage and variable change .

[jonnoj2222]

The likelihood of choosing the wrong door is 2/3. Thus, mathematically, there is a 2/3 chance that you DONT have the prize but the game show host does. The opening of one of the doors by the game show host is a useless factor. It doesn't change the original fact that the host have a higher likelihood of holding the prize then you do.

[mumiscrunk]

@DementedlyHappy I found that explanation animated on stayorswitch (dot) com, it has 100 doors, but it's a good explanation.

[reefreep]

After you choose your first door, the chances of picking the money are 33%, while you picking one of the empty doors 66% (therefor you are probably on an empty door). After he opens an empty door, it is in your interest to switch because him opening the door did nothing. There is still a 66% chance that the current door you are on is empty. So, you should switch because if you do, the chances of you ending up with the money is 66% instead of 33%.

[kirkbocek]

If you'd like another way to prove the correct answer to the Monty Hall Problem, see my video "Proving the Monty Hall Problem."

[133j0hn]

The Monty Hall problem breaks down to this simple question:

"Would you like to have 1 door or 2 doors? If you choose 2 doors, I’ll give you the better prize of those 2 doors. If you choose 1 door, you’ll be stuck with your choice."

The choice becomes obvious.