3 door riddle

[Tomsan]

ok for the ones who know this one plz keep it to yourself for a while..

its seems like a paradox but it isnt really here's the riddle:

You are a finalist in a game show, you are presented with 3 doors, behind one is a brand new mercedes behind another a paper bag and behind the other one lies a candybar..

you must make a choice between the 3 doors after you have taken the choice the game-host opens one door showing either the paperbag or the candybar. NOw you are allowed to switch between the two remaining doors.

would you switch???

[mranarchy]

You switch...some confusing shit in maths makes it so you double your chances when you do

(derren brown FTW!)

[solardave]

At 5/20/08 04:15 PM, Tomsan wrote:
You are a finalist in a game show, you are presented with 3 doors, behind one is a brand new mercedes behind another a paper bag and behind the other one lies a candybar..

you must make a choice between the 3 doors after you have taken the choice the game-host opens one door showing either the paperbag or the candybar. NOw you are allowed to switch between the two remaining doors.

would you switch???

Well by your story I have made a choice. One other door is opened and it shows either the paperbag or candybar. Now behind that door is either the paperbag or the candybar so surely I have chosen the Mercedes.
I wouldn't switch.

I don't expect this to be right.

[Tomsan]

ok.. no
change the paperbag and candybar into two scissors.. so 1 mercedes 1 scissor 1 scissor

what I meant is that when the gamehost opens a door he opens a 'bad' choice.

[Vile-Pudding]

Switch

First your chances of getting the car are 1/3, so you can assume that you don't choose it.

Now that you have assumed that one of the other doors contains the car, you can choose one of the remaining two doors with a 1/2 chance of getting the car.

You still have a 1/3 chance of getting a car on the first choice, but you have a 1/2 chance of getting it on the switch.

[Kunera]

It wouldn't matter either way.
You would still have a 1/2 shot either way.
Since you know one of the 3 doors is revealed to have the 'bad' choice, you know that it's no longer a choice.

Either the first door you picked, or the one you could switch to, has the Mercedes.
As far as you know, there's a 50-50 shot either way.
It's just human nature to want to switch, apparently.

[Tomsan]

At 5/20/08 04:46 PM, Kunera wrote: It wouldn't matter either way.
You would still have a 1/2 shot either way.
Since you know one of the 3 doors is revealed to have the 'bad' choice, you know that it's no longer a choice.

Either the first door you picked, or the one you could switch to, has the Mercedes.
As far as you know, there's a 50-50 shot either way.
It's just human nature to want to switch, apparently.

nope its math..
when the situation occurs, the better choice is to switch making your winning chances 2/3 instead of 1/3.

ill place a diagram

[Phantox]

He showed me the one EITHER with the bag or the candy? Well I would just pick the one he didn't open.

[FullArsenal]

I wouldn't want to switch, because I'm like that. And this isn't a riddle.

[Tomsan]

lets say you would choose door number one in all situations; u see that if you switch; your winning chances are 66.66% while if u stay they remain 33.33%

[FullArsenal]

At 5/20/08 06:05 PM, Tomsan wrote: lets say you would choose door number one in all situations; u see that if you switch; your winning chances are 66.66% while if u stay they remain 33.33%

So you mean switch to two cars and 1 scissors? You make no sense.

[Tomsan]

At 5/20/08 06:07 PM, BenjaminBigelow wrote:

At 5/20/08 06:05 PM, Tomsan wrote: lets say you would choose door number one in all situations; u see that if you switch; your winning chances are 66.66% while if u stay they remain 33.33%

So you mean switch to two cars and 1 scissors? You make no sense.

dude? read the first post.. u are able to switch after your initial choice and after the gamehost opened one door with a scissor.

the upper diagram shows the winning chances when u choose not to switch and the lower when you choose to switch doors

[FullArsenal]

At 5/20/08 06:10 PM, Tomsan wrote:

the upper diagram shows the winning chances when u choose not to switch and the lower when you choose to switch doors

You have two doors
The car is behind one
Either way, there's a 50% chance.

[Tomsan]

At 5/20/08 06:11 PM, BenjaminBigelow wrote:

At 5/20/08 06:10 PM, Tomsan wrote:

the upper diagram shows the winning chances when u choose not to switch and the lower when you choose to switch doors

You have two doors
The car is behind one
Either way, there's a 50% chance.

nope its 66.66
most people dont accept it because it goes in opposite direction of their 'intuition' but if the situation occurs (like I described it) your winning chances are increased.. look at the diagram its easy

[kustdro]

I'd want the paper bag myself, so I'm set.

[Tomsan]

in the same context:

if your friend, who you havent seen for 10 years, tells you that he has got two children and one of them is a boy, the chances of the other kid being a girl is 2/3 while it being a boy is 1/3

B-B
B-G
G-B
G-G

one is a boy so possibilities

B-B
B-G
G-B

the chance that the other one is a girl is 2/3

pretty weird eh?

[RageVI]

I have never seen somebody struggle so much to divide 1 by 2 as you.

If the game show host shows you one of the "crap prize" doors, that means there's two doors left to choose from. One has the car, the other doesn't.

Two doors.

One has the car.

One out of two doors has the car.

1 / 2 = 50% chance. Doesn't matter if you switch. You can only choose one.

Also your chart is nothing more than a chart.

God knows why I'm even posting here. It's probably because the time of day. I'll just lock this if people make fun of you too much.

[penterz]

Rock beats scissors

[Tomsan]

At 5/21/08 07:32 AM, RageVI wrote: I have never seen somebody struggle so much to divide 1 by 2 as you.

1 / 2 = 50% chance. Doesn't matter if you switch. You can only choose one.

Also your chart is nothing more than a chart.

God knows why I'm even posting here. It's probably because the time of day. I'll just lock this if people make fun of you too much.

lol!

I know it seems simple, but you really are WRONG.
if i cant manage to comprehend it here are some links.. its a know 'paradox' (its not really paradox, but more a counter intuitive thingy..

check out the links:

one This one actually has a little test applet in it

number 2

number 3

wiki

I can go on and on. so plz dont do the "I am a though smart mod, and you are stupid" act

[Togukawa]

At 5/21/08 07:32 AM, RageVI wrote: I have never seen somebody struggle so much to divide 1 by 2 as you.

If the game show host shows you one of the "crap prize" doors, that means there's two doors left to choose from. One has the car, the other doesn't.

Two doors.

One has the car.

One out of two doors has the car.

1 / 2 = 50% chance. Doesn't matter if you switch. You can only choose one.

Also your chart is nothing more than a chart.

God knows why I'm even posting here. It's probably because the time of day. I'll just lock this if people make fun of you too much.

You're wrong. 50% chance would be true if you are a complete idiot and totally forgot about what went on before your second choice. The statistical clue is that the two choices (first and second one), are NOT unrelated, which makes the second choice be different from the vanilla 1/2 odds you have in an independent experiment.

It's actually quite simple. You make the first choice: you have 1/3 odds of picking the mercedes, because there are 3 doors. Then host does some shit, and you get a second choice: namely to switch. So if you were wrong the first time around (1/3 chance), and then you switch, you become right. So by switching you have 2/3 chance of getting the mercedes, if you stay by your first choice, the second choice basically did jack shit at all, and you remain with your first choice, which had 1/3 chance.

Another way to look at it: At first you had 1/3 odds of being right. By someone offering you a second choice, and not actually doing anything with it, your odds of having been right the first time can't just increase to 1/2.

[metalstorm]

At 5/21/08 07:32 AM, RageVI wrote: I have never seen somebody struggle so much to divide 1 by 2 as you.

If the game show host shows you one of the "crap prize" doors, that means there's two doors left to choose from. One has the car, the other doesn't.

Two doors.

One has the car.

One out of two doors has the car.

1 / 2 = 50% chance. Doesn't matter if you switch. You can only choose one.

Also your chart is nothing more than a chart.

God knows why I'm even posting here. It's probably because the time of day. I'll just lock this if people make fun of you too much.

Actually I think you'll find that Tomsan is correct when he says your chance of winning is 66% when you switch doors. This is the
Monty Hall Problem and any website that talks about it will tell you that if you switch doors you will have a 66% chance of winning the car although most people assume that it can only possibly be a 50/50 chance that you win because you're ultimately only choosing between two doors. I'll try to explain how it works.

You have 3 doors labeled a,b and c.

I choose door a which means that I have a 1 in 3 chance that I've chosen the right door. At this stage the host opens door b to show me that the prize is not behind that door. Whats crucial here is the fact that I only initially had a 1 in 3 chance of picking the right door and that I know that door b does not contain the prize which means that I have a 2 in 3 chance of winning if I pick door c and not a 50/50 chance. If you still don't understand you can follow the link I provided. it may explain it better.

[gr33k-prty-b0y]

the answer is you should change but I disagree...

3 doors 33% chance
2 doors = 50% chance

switching doesnt create better chance

[XxRandomdmxX]

this is confusing... but id say i stay with the current thing that i chose.

[metalstorm]

At 5/21/08 08:00 AM, gr33k-prty-b0y wrote: the answer is you should change but I disagree...

3 doors 33% chance
2 doors = 50% chance

switching doesnt create better chance

It does actually because the two choices you make are not independent of each other. With the first door you choose you have 1/3 chance of being right. then one wrong door is revealed leaving one door left and because all probabilities have to add up to one this means that the chance of the final door being the right one must be 2/3 hence you have a 2/3 chance of winning if you switch.

[Togukawa]

It's confusing because there are so little doors.

Imagine the same experiment, but with about a billion doors. You make a choice out of a billion doors, virtually being certain you are wrong. Then the host opens every single door, except the door that you chose, and another door.

I'd definitely switch :)

(Here you see the clue again, the host isn't free to choose which door he leaves closed, if you made the wrong choice the first time, he is FORCED to have the "switch door" be the correct door. Only if you were lucky and picked the correct door the first time, then the host is allowed to pick any door. The two choices aren't independent, hence the chance for the second choice isn't 50%)

[Stevezor]

Funny, I just learned about this yesterday at school. What the fuck.

Anyways, I would switch. Better chance at getting it.

[Objection]

At the start, you have a 33% chance of getting the car and a 67% chance to pick a bad prize. One of the bad prizes is removed from the mix and you are given a choice between switching and sticking. This is essentially the same as having a choice between one car and one bad prize, and assuming that the car and bad prize were arranged randomly, the chance of getting the car is 50% and the chance of getting the bad prize is 50%.

[Kuro]

I always think of it like this.

If you choose one of the doors, another one of the doors is taken out, right?

And if you stay with that same door, that's you with a 1/3 chance of winning.

However, if you change, you can think of it like this.

If the person instead of showing you which of the other two contained the crap prize, just told you that that one was eliminated, and you had the option of switching to the one that isn't eliminated, then that means that switching is the equivalent of choosing the two remaining doors.

Therefore you have a 2/3 chance of winning if you switch.

Badly explained, but that's how I see it.

[Objection]

At 5/21/08 08:23 AM, Kuro wrote: If the person instead of showing you which of the other two contained the crap prize, just told you that that one was eliminated, and you had the option of switching to the one that isn't eliminated, then that means that switching is the equivalent of choosing the two remaining doors.

Then, for all the contestant knows, the car has gone.

[LazyPint]

The easy way to explain it is to ignore the fact that the door has been opened.

3 doors. You pick one and I say "Do you wish to switch to the other two doors? If the car is in either, you win it."

At the end of the day, you already know that one of the other doors contains a lose. Opening one and showing yo that tells you nothing you didn't already know.