Logic problem

[GofG]

No googling!

You are on a game show. You are presented with three doors. Behind one is a car; behind the other two are donkeys.

You choose door #1.

The game show host offers to show you one of the doors with a donkey behind it; you accept. He opens door #2 and reveals a donkey.

The game show host offers you the chance to switch to door #3.

Do you take it? Why or why not?

 

[teeman92]

there should be a car in door 1 riiiight?

 

[GofG]

Not necessarily. The car could be behind door #1 or #3. Does switching to door #3 improve your chances? Think about it.

 

[hat!]

Isn't this from the movie 21? I love that movie.

 

[The Sauce Boss]

You switch it.

 

[Grandeza]

I don't think it would improve your chances, but heh maybe I'm wrong. Someone enlighten me.

 

[.AC.]

http://en.wikipedia.org/wiki/Monty_Hall_problem

its a famous logic problem.

 

[Mini Mic]

I seem to remember this from school, you're supposed to switch it because you initially had a 1/3 chance of getting it right but by the elimination of one door you now have a 2/3 chance, ergo changing increases the likelihood of success, right?

 

[Mota]

LOL, I think I got it!

Spoiler

"Behind ONE is a car" I choose door one.

Simple enough

 

[Mazaloth]

Coincidently this was in a book I read.

You have 2/3 chance of obtaining a car.

So yes, I would.

The curious incident of the dog in the night. Or something like that.

 

[Overload]

Yes, this is from the movie 21. Like Mic128 said, you're supposed to switch because you now have a 1/2 chance of guessing correctly. I still don't see the point though, as each of the doors have a 1/2 chance of being the correct choice.

 

[n88]

Do I get to keep whatever's behind the door? Otherwise I don't really care.

 

[StealthyGunnar]

Switch. You currently have a 33.33% chance to win. With the 2nd door being out, you now have 66.66% that door 3 will have the car. Thanks for the other 33.33%.

 

[Limey]

I just read that wikipedia article on the thing. That's fascinating.

 

[highfive]

it seems like switching wouldn't work in real life but there's the math to prove it. I would Imagine having that in your favor would work more or less 3/5 times right?

 

[D20]

The solution is difficult to explain. In fact, the solution is different depending on whether you are looking at the entire problem or not. Most people will just look at the second half, where there is a 50/50 chance of winning the car. They will then claim that the switch does not matter, which would be correct.

However, the problem did not begin with this such probability. At the start, there are 3 choices, thus a 1/3 chance of winning. That means the chances of losing are 2/3... which is significantly greater. When the host strikes one option after your initial choice, he is actually asking you "did you guess right or wrong?" Since you initially had a 2/3 chance of guessing wrong, you should assume you chose incorrectly and switch. Essentially, this creates a probability reversal. It affords you the 2/3 chance.

 

[Teczer0]

This messes with my head >.<

Really fun question though. I definitely thought at first that it didn't matter. I didn't think about how the first pick gave you some information or something to that extent... I think.

 

[wool]

Simple math proves that switching does help your chances...just take all of the cases and do it in your head. its really simple.

But thats assuming that the gameshow always shows you a donkey. If he actually points to a random door not knowing whether it is a donkey or not then switching or not switching doesn't matter.

 

[Da Shuffla]

Truth. This problem works on the assumption that the first door you chose had the donkey. Therefore, the one left after one is taken out must be the car.

 

[Overload]

The solution is difficult to explain. In fact, the solution is different depending on whether you are looking at the entire problem or not. Most people will just look at the second half, where there is a 50/50 chance of winning the car. They will then claim that the switch does not matter, which would be correct.

However, the problem did not begin with this such probability. At the start, there are 3 choices, thus a 1/3 chance of winning. That means the chances of losing are 2/3... which is significantly greater. When the host strikes one option after your initial choice, he is actually asking you "did you guess right or wrong?" Since you initially had a 2/3 chance of guessing wrong, you should assume you chose incorrectly and switch. Essentially, this creates a probability reversal. It affords you the 2/3 chance.

This clears things up.

 

[Mewter]

No googling!

You are on a game show. You are presented with three doors. Behind one is a car; behind the other two are donkeys.

This gave it all away.
No, just kidding.

 

[sammy p]

You are on a game show. You are presented with three doors. Behind one is a car; behind the other two are donkeys.

i figured it out!!! although im sure im not the first one....:embarrass
but i didnt read the other responses so its like i figured it out on myown right?? lol

 

[½NIÇK½FBM]

In a village there is barber. This barber shaves those and only those who do not shave themselves.

Who shaves the barber?


First figure out the paradox, then figure out the answer. It took me about 30 minutes.

 

[Jonkku]

Duh.. There's another barber and they shave each other, quite obvious..
Took me ten seconds.

 

[Mewter]

In a village there is barber. This barber shaves those and only those who do not shave themselves.

Who shaves the barber?


First figure out the paradox, then figure out the answer. It took me about 30 minutes.

The people who do shave themselves shave the barber?
Are you sure you worded it correctly?
Lol, another barber.

 

[½NIÇK½FBM]

Duh.. There's another barber and they shave each other, quite obvious..
Took me ten seconds.

HA! But if the barber doesnt shave himself that means he must shave himself because he only shaves people who DONT shave themselves!




Let me go inot more detail.......


"In a village there is barber. This barber shaves those and only those who do not shave themselves.

Who shaves the barber?"

You said theres another barber that shaves the original barber right? But in my statement I said the barber shaves those and only those who dont shave themselves. So if another barber shaves the original barber, that means the original barber doesnt shave himself so he is forced to shave himself.......

 

[Mewter]

HA! But if the barber doesnt shave himself that means he must shave himself because he only shaves people who DONT shave themselves!

So his wife shaves for him?
No idea.

 

[½NIÇK½FBM]

If the barbers wife shaves him that means he doesnt shave himself but he must shave those and only those who dont shave themselves.

 

[Elder Sister]

donkey thing was easy, knew the answer before even reading the question.
never understood it though

@barber thing
is it stated that he must shave all those who dont shave themselves?
if not, then its obvious....

 

[Jonkku]

Well, he clones himself and then shaves the clone and vice versa, they're technically the same person, but some would say that they are different people.
[/random-theory]

And yeah, your didn't mention at first that he's forced to shave everyone who doesn't shave themselves..

 

[Xivii]

I would keep the same door because I decided I want the Donky

Spoiler

Kong.

 

[Fuelbi]

i heard the 3rd door has a 66% chance of happening

 

[Moy]

Riding a donkey as your main mode of transportation would be creative, so you really can't lose.

And naming a donkey isn't as weird as naming a car.

 

[StinkomanFan]

Switch. You currently have a 33.33% chance to win. With the 2nd door being out, you now have 66.66% that door 3 will have the car. Thanks for the other 33.33%.

No, You'd have a 50% Chance. MATH DOESN'T WORK LiKE THAT!

 

[½NIÇK½FBM]

The answer to my barber question is.........nobody shaves the barber. He is bald.

 

[Elder Sister]

you kiddin are you?
foolin usT_T

 

[Hydra.]

Ah this is hurting my brain! But I wouldn't switch because I would feel like he was trying to get me off of the winning door or something.

 

[uhmuzing]

It's to your advantage to switch when he offers.

 

[Tacel]

Pick door #2 because donkeys are cooler than cars.

 

[Mr.Lombardi34]

You pick a door. There are two doors left. There's a 2/3 chance that one of the other two contains the car. One of the other two is eliminated, therefor the remaining one has a 2/3 chance of winning while the one you picked only has 1/3.

...Just switch, you don't have to understand it