The Monty Hall - Lets Make a Deal problem

[TallBill]

In a certain game show, a contestant is presented with three doors. Behind one of the doors is an expensive prize, behind the others are junk (or goats). The contestant is asked to choose a door. The game show host, Monty, then opens one of the other doors to reveal a junky gift behind it. The contestant is then asked if she/he would like to stick with the original door or switch to the remaining door.

Should the contestant...
- Stick with his original door
- Swich doors
- It doesn't matter, its 50/50

Ok, TONS of flaming, arguing and bitterness will come from this, but maybe you'll learn something. I wont make a poll because people will flip flop as they figure it out. This is a hugely debated statistic problem, and extremely easy once you grasp it. I'm going to stay out of it for now since I figured out the correct answer the last time this was posted.

 

[MikeyIs4Dcats]

50/50. He knows one of 2 goat door, but knows nothing about the other one or the prize door.

 

[ggnl]

Isn't it a 50/50 chance? I'm guessing it isn't, or it wouldn't be a subject for debate...

 

[thelanx]

Easy, he should switch, since the chances of him being right are 1/3 since he guessed blindly. Thus once one of the junk doors is revealed, the other door has a 2/3 chance of being the expensive prize.

 

[blackdogdeek]

iirc, he should switch to the other door.

 

[sygyzy]

It is definitely not 50/50. I believe the answer is what thelanx stated.

 

[MikeyIs4Dcats]

Originally posted by: thelanx
Easy, he should switch, since the chances of him being right are 1/3 since he guessed blindly. Thus once one of the junk doors is revealed, the other door has a 2/3 chance of being the expensive prize.

As does his original door using that logic.

 

[Brutuskend]

"It's officer O'Malley of the F.B.I., you're BUSTED!"

"Should'a taken the REDS man!"

 

[TallBill]

Originally posted by: Brutuskend
"It's officer O'Malley of the F.B.I., your BUSTED!"

"Should'a taken the REDS man!"

*runs* AHHHHH!!!

 

[amoeba]

its switch doors.

I'll provide a more indepth proof later.

 

[DainBramaged]

I don't know, however, it sounds interesting.

 

Switch doors. The answer has been explained above. A high school math teacher of mine covered it more thoroughly, but I can't remember what he said. But the answer is "switch."

 

[fs5]

switch doors.

 

[Ikonomi]

You should switch, because Monty always opens a door with a goat behind it. If the door he opened was random, then it wouldn't matter if you switched or not.

But as it stands, the first time you pick, you have a 1/3 chance of getting the prize. After Monty opens one of the goat doors, you have another chance to pick, giving you a 2/3 chance of picking the car if you pick the other door. If you stick with your original choice, you only got to pick a door once, and you're stuck with a 1/3 chance.

 

[Toasthead]

Its easier to understand if you think of it like this...

Pick one card out of 100 that you think has a star on it ( only one card does)
now I re turn over 98 of the cards which dont have a star on it, leaving your card and another card not turned over. Now do you think your card has the star or the other card?

 

[Zeeky Boogy Doog]

Originally posted by: Toasthead
Its easier to understand if you think of it like this...

Pick one card out of 100 that you think has a star on it ( only one card does)
now I re turn over 98 of the cards which dont have a star on it, leaving your card and another card not turned over. Now do you think your card has the star or the other card?

that one is easy, i'm switching cards

same for the other one, switch

 

[dullard]

Interesting I just posted a link that is very much related to this today in the pi thread (note that specific link doesn't mention LMAD, but other pi calcation links with Monte Carlo almost all do). I used this problem to teach the Monte Carlo method in my chemical engineering computations class. The answer is easy to find by a number of methods, but I really like the Monte Carlo method (and all methods say to switch).

 

[edmicman]

So what happens if you switch and the first door you picked has the prize? You look like an idiot.

 

[amoeba]

Originally posted by: edmicman
So what happens if you switch and the first door you picked has the prize? You look like an idiot.

uh, not really. you went for the one that probabilistically had the highest chance of you winning.

 

[eigen]

Originally posted by: dullard
Interesting I just posted a link that is very much related to this today in the pi thread (note that specific link doesn't mention LMAD, but other pi calcation links with Monte Carlo almost all do). I used this problem to teach the Monte Carlo method in my chemical engineering computations class. The answer is easy to find by a number of methods, but I really like the Monte Carlo method (and all methods say to switch).

You teach MCMC's.Cool.I like those.The coupling method is a beatiful proof technique.

 

[Demon-Xanth]

Possible situations:
Prize behindoor pickoor revealed:Wins if he stays/swaps
1:1:2or3:Stay
1:2:3:Swap
1:3:2:Swap
2:1:3:Swap
2:2:1or3:Stay
2:3:1:Swap
3:1:2:Swap
3:2:1:Swap
3:3:1or2:Stay

Out of 9 initial possibilities, 6 will win if swapped, 3 if stay.