http://www.deanesmay.com/archives/000601.html
Offers a good read, still can't figure out why it's like choosing twice. I made a little Monte Carlo sim and it's at 150,000 trials with 100,068 wins (about 2/3). Strange...
Mensa Level Brainteaser
Moderator: MaxCoderz Staff
-
Jim e
- Calc King
- Posts: 2457
- Joined: Sun 26 Dec, 2004 5:27 am
- Location: SXIOPO = Infinite lives for both players
- Contact:
I can't believe this guy got so melodramtic for simple math. Whats worse is how so many people posted not understanding and frying there brains to explain the reasoning. I truly doubt many mensa members got thrown off by this.
--------spoiler----------
Your odds of picking the wrong door first are 2:3
Knowing that you assume the first door you pick is wrong.
When monty reveals the other wrong door, with you assumption that your door is wrong you switch to the other.
Since that other door is the only other choice it's odds are 2:3 that this door is the correct door.
And your first choice still has 2:3 odds that its wrong.
If you don't switch doors then your odds remain what they initially started with, 1:3
Chances are you would win if you switch and lose if you don't.
It may only be confusing because you dont see the purpose of picking 1 of 3 doors and having monty remove one, and picking randomly between two doors. But there is a difference because your initial odds are different. By switching you are basicly picking the 2 wrong doors and elimnating them.
--------spoiler----------
Your odds of picking the wrong door first are 2:3
Knowing that you assume the first door you pick is wrong.
When monty reveals the other wrong door, with you assumption that your door is wrong you switch to the other.
Since that other door is the only other choice it's odds are 2:3 that this door is the correct door.
And your first choice still has 2:3 odds that its wrong.
If you don't switch doors then your odds remain what they initially started with, 1:3
Chances are you would win if you switch and lose if you don't.
It may only be confusing because you dont see the purpose of picking 1 of 3 doors and having monty remove one, and picking randomly between two doors. But there is a difference because your initial odds are different. By switching you are basicly picking the 2 wrong doors and elimnating them.
-
tr1p1ea
- Maxcoderz Staff
- Posts: 4141
- Joined: Thu 16 Dec, 2004 10:06 pm
- Location: I cant seem to get out of this cryogenic chamber!
- Contact:
Yes, you have a better chance of winning if you switch.
At first glance i thought that it was 50/50 because you would regard the incorrect door in which you were shown and basically the competition starts again.
But then i realised that if you look at it from the start of the competition, you have a better chance of initially picking an incorrect door. This means that Monty MUST show you the remaining incorrect door, and if you switch ... you win! So by there being a better chance of you initially picking the incorrect door, you have a better chance of winning in the end! ... At least thats how i see it
.
At first glance i thought that it was 50/50 because you would regard the incorrect door in which you were shown and basically the competition starts again.
But then i realised that if you look at it from the start of the competition, you have a better chance of initially picking an incorrect door. This means that Monty MUST show you the remaining incorrect door, and if you switch ... you win! So by there being a better chance of you initially picking the incorrect door, you have a better chance of winning in the end! ... At least thats how i see it
."My world is Black & White. But if I blink fast enough, I see it in Grayscale."
-
Guest
It's a lot simpler if you view it as though it had 1000000 doors, with Monty (Monte?) showing you 999998 of them.
Your chances of guessing correctly the first time is 1:1000000, with odds of getting it incorrectly being 999999:1000000. With a switch, you would win this 999999 out of 1000000 tries because you would only guess it right on the first try 1 out of 1000000 times. Think about it, cause I'm confused with my explanation... but I get it!
Your chances of guessing correctly the first time is 1:1000000, with odds of getting it incorrectly being 999999:1000000. With a switch, you would win this 999999 out of 1000000 tries because you would only guess it right on the first try 1 out of 1000000 times. Think about it, cause I'm confused with my explanation... but I get it!
I made a visual explanation if you still don't know why it's 2/3 chance.
[Gridwars Score] - E: 1860037 M: 716641 H: 261194