My Favorite Thinking Problem...

[Laeelin]

In a game show, a contestant is given a choice of three doors of which one contains a prize. The other two doors contain a chicken. After the contestant choses an initial door, the host of the show then reveals an empty door among the two unchosen doors, and asks the contestant if he or she would like to switch to the other unchosen door.

The question is should the contestant switch.


It's not a trick qestion either. =)

[BobbySalami]

Yes....I have a chicken lovers website.

[hydroseeds]

To get to the other side?

[vqc]

technically yes the contestant should switch.

although there have been millions of issues with this question, and it has been talked to death. the general idea is that:
on ur first try you ahve 1/3 chance to get it right. On the second try you have a 1/2 chance. So by not switching you have given urself only a 33% chance of getting it correct.

[a500lbgorilla]

There's no point to switching.

If he picks door 1 and reveals door 3 all that happens is either Door 3 is the prize and it doesnt matter if he switches or door 3 is a chicken and he's 50/50 to pick the right door (and his initial pick is just as viable)

Unless he can switch to door 3 after revealing it, there's no point.

-'rilla

[Laeelin]

on ur first try you ahve 1/3 chance to get it right. On the second try you have a 1/2 chance. So by not switching you have given urself only a 33% chance of getting it correct.

Incorrect....

There's no point to switching.

If he picks door 1 and reveals door 3 all that happens is either Door 3 is the prize and it doesnt matter if he switches or door 3 is a chicken and he's 50/50 to pick the right door (and his initial pick is just as viable)

Unless he can switch to door 3 after revealing it, there's no point.

Incorrect..

I'll explain it blow, scroll down if your ready for the answer..

With your first choice, you have (A) (B) (C) .. 1/3 chance that it's behind each door...

(A) = 1/3
(B) = 1/3
(C) = 1/3

So you have a 1/3 chance it's the door you pick, and a 2/3 chance that it's behind one of the other two doors.

(A) = 1/3
(B) or (C) = 2/3

You pick (A)

The game show host opens one of the remaining doors to show (and this is the key) WHICH of the 2 remaining doors (with a 2/3 chance it's behind one of them) is the incorrect one.

(A) = 1/2

(B) or (C) = 2/3

Shown it's not (B) leaves the 2/3 chance behind door (C)

Another way to look at it is this:

If you always change, you can only lose if you start with the winning door (and we all agree you have a 1/3 chance of starting with the loseing door)

for example:

you pick door (A) and it's behind door (A) then the host opens door (B) or door (C) (either one) and you change to the other, you lose.

You pick door (B) and its behind door (A), he opens (C), you change to (A), you win

You pick door(C) and its behind door (A), he opens (B), you change to (A), you win.

I wrote a program that actually runs the problem if you want to see:

http://www.startingdreams.com/doors.php

If you dont believe that, take 3 cups, put a coin in one, have a friend mix them up, you pick one, have him show you an empty cup from the remaining two, and then write down how often you win if you stay, and how often you win if you change...

[Laeelin]

Another way to look at it is this:

You have 100 doors, one has a car, 99 have nothing...

You pick door (A) and the host opens 98 doors showing chickens.

Do you still think there is a 50/50 chance that the door you started with is the correct one?

[Greedo017]

i hate this question.

once time i told this to a couple friends, and this one friend is this arrogant idiot and kept INSISTING that i was wrong. i just told it to tell it because its tricky, but it ended up with 3 people yelling at me about how wrong i was.... after a while, i actually got out cups and put a ball under the first one, then the second one, then the third one. if you act this out and write down the results, even just 3 times, you will see how totally obvious the answer is. but they still didn't get it for like 3 days...... oh well.

[Miffed22001]

at least you can talk to the chicken

[a500lbgorilla]

Another way to look at it is this:

You have 100 doors, one has a car, 99 have nothing...

You pick door (A) and the host opens 98 doors showing chickens.

Do you still think there is a 50/50 chance that the door you started with is the correct one?

Yes, becuase you see two doors and one has a car in it and the other does not. No one is ever going to convince me otherwise. It's an entirely new event that you must treat as stand alone.

Just like you're presented 2 doors and one has a car and the other doesnt, you pick A and win a car. Congratz.

-'rilla

[DaNutsInYoEye]

You guys really shouldn't be playing this game without the proper bankroll for it.

[a500lbgorilla]

Also, does he always open a door with a chicken in it?

-'rilla

[Laeelin]

Also, does he always open a door with a chicken in it?

-'rilla

Yes, but that actually doesnt matter =)

Yes, becuase you see two doors and one has a car in it and the other does not. No one is ever going to convince me otherwise. It's an entirely new event that you must treat as stand alone.

Just like you're presented 2 doors and one has a car and the other doesnt, you pick A and win a car. Congratz.

-'rilla

Let me try a more extreme example then....

Pretend you have a friend that is a time traveler from the future.

He sees you buy a lottery ticket and looks at your numbers.

You Picked: 08-14-19-24-29-32 (Door A)

He then says, well, i'll give you a hint... out of the millions of possible numbers (millions of other doors), it's either the numbers you picked already, OR (opens all but one of the millions of other doors) the number is:

05-15-17-20-21-24 (the other door remaining)

Do you still think it's a 50/50 chance between thoes two numbers (Doors)?

ps: if you still dont see it, try using cups and a penny.. It's 100% true, really... I didnt make this question up... It's not just a math trick, it's real life fact! =)

[a500lbgorilla]

Alright, wow. That lottery example worked really fucking well. It just clicked. You are truely my better this day.

-'rilla

[Laeelin]

You are truely my better

potd!



You didnt hear this from me, but I wrote the script I linked to prove it wrong

[SinkRox]

I change my mind and pick the door the cute host showed me, because there's a chicken behind two doors and a prize in the other.. seeing as the door she showed me was empty it must be the prize door.

*thinking outside the box*

[nomofoshobro]

In a game show, a contestant is given a choice of three doors of which one contains a prize. The other two doors contain a chicken. After the contestant choses an initial door, the host of the show then reveals an empty door among the two unchosen doors, and asks the contestant if he or she would like to switch to the other unchosen door.

The question is should the contestant switch.


It's not a trick qestion either. =)

If the host opens one of the remaining doors and it is empty, then he is a lying bastard. it should have either a chicken or the prize.

[arkana]

There is a 1/3 chance that you pick the right door with your first pick and 2/3 chance that the right door is one of the remaining two. You know which one of the two remaining doors will be the right door if your first choice was incorrect (because the host opens one of them). Therefore it makes sense that you should switch because 66% of the time your first choice will be incorrect which means that 66% of the time the other door is the correct one.

[Irisheyes]

So... Eh... What was the prize?

[lamaros]

Two chickens.

[Irisheyes]

Two chickens.

Funky.
























Chicken.

[Miffed22001]

if i were a goldfish reading this thread i woulda forgotten what it was about by now

[Irisheyes]

What thread?

[Jeebus Kliest]

I was always pretty damn sure that with false back walls they would just switch the prize and the chicken just to screw most of the people.

[chardrian]

You forgot to say that the host always shows a chicken before asking if the contestant wants to switch.

The answer is switch.

You have a 2 in 3 shot of winning if you switch. A 1 in 3 shot if you don't.

It's purty easy to see - let's say you choose door one and let's check out the three possibilities.

1) Prize is behind door 1. He shows you either door 2 or 3, you switch and lose.

2) Prize is behind door 2. He has to show you door three (since obviously you will change if he shows you your losing door) you switch and win.

3) Prize is behind door 3. This time he has to show you door 2 (see above for why), you switch and win.

[Laeelin]

You forgot to say that the host always shows a chicken before asking if the contestant wants to switch.

That part doesnt matter... It only matters that the chicken was shown in the example =)

[TylerK]

...one contains a prize. The other two doors contain a chicken.

After the contestant choses an initial door, the host of the show then reveals an empty door among the two unchosen doors

Rigged

[Miffed22001]

im gona shoot those bastard chickens!!!!
argghhhhh :P