Three Little Boxes

[Jayhawker Soule]

A red, green and brown box is placed on the table in front of you. Two are filled with sand and one with an equivalent weight of gold.

You select the brown box, which remains closed.

You are then shown that contents of the red box which is (of course) filled with sand.

You are then given the option of keeping the brown box or switching to the green.

Vote ...

 

[4consideration]

Keep the brown box.

 

[Revoltingest]

I'd heard this one before.
As presented to me, I still don't get the 'correct' answer.
(I'll hold off on my reasoning, lest I pollute the thread with my efforts.)

 

[Marble]

I keep the brown box.
Reason is, that I would be angry that I did not take the green box finding out that it contains the gold - but I would be even much more angry if the brown box contains the gold and I gave it away.

 

[Iti oj]

Green because its the color of my eyes lol

 

[Jayhawker Soule]

I keep the brown box.
Reason is, that I would be angry that I did not take the green box finding out that it contains the gold - but I would be even much more angry if the brown box contains the gold and I gave it away.

:foryou:

 

[bobhikes]

A red, green and brown box is placed on the table in front of you. Two are filled with sand and one with an equivalent weight of gold.

You select the brown box, which remains closed.

You are then shown that contents of the red box which is (of course) filled with sand.

You are then given the option of keeping the brown box or switching to the green.

Vote ...

Keep brown box as the person either knows whats in the box (which they have openned the red box to try and trick me) or the the person has no idea and my odds on the brown box just went from 33% to 50%.

 

[lunakilo]

A red, green and brown box is placed on the table in front of you. Two are filled with sand and one with an equivalent weight of gold.

You select the brown box, which remains closed.

You are then shown that contents of the red box which is (of course) filled with sand.

You are then given the option of keeping the brown box or switching to the green.

Vote ...

probability that the green box is the one with the gold is 2/3 so of course I would switch

This one is soooooooooooo oooooooooooold

 

[bobhikes]

probability that the green box is the one with the gold is 2/3 so of course I would switch

This one is soooooooooooo oooooooooooold

Your first choice is 1/3

Your second choice is 1/2

They are 2 independent choices they don't add up.

Thats like saying I buy a lottery ticket 1 out of 100
They miss print 1 number so they delete the number offer me the chance to trade in for another number or keep my own.
My odds are now 1 out of 99 and no better if I trade in the ticket.

What I have seen on-line is a game show host. A game show host is going to know where the big prize is and not select to show it. In my mind your odds in this case are always 50/50 and you never actually have the 1/3 chance because he wants to entertain and build drama.

Just to see the answer is flawed use 4 boxes and take one and show one

Blue, Red, White and Yellow.

You take the white
He show's the yellow.

What's the probability for the Blue and Red and your white remember they have to add to 100%

 

[lunakilo]

Your first choice is 1/3

Your second choice is 1/2

When you first choose the brown box, you have no knowledge of what is in either of the boxes, so the probability that the brown box contains gold is 1/3

The probability that the green OR the red box contains gold is 2/3.

He now shows you that the red box does not contain gold.
The probability that the green OR the red box contain gold is still 2/3, but since you now know for certain that thered box dos not contain gold...

Get it?

brown = 1/3
red = 0/3 = 0
green = 2/3

They are 2 independent choices they don't add up.

Thats like saying I buy a lottery ticket 1 out of 100
They miss print 1 number so they delete the number offer me the chance to trade in for another number or keep my own.
My odds are now 1 out of 99 and no better if I trade in the ticket.

What I have seen on-line is a game show host. A game show host is going to know where the big prize is and not select to show it. In my mind your odds in this case are always 50/50 and you never actually have the 1/3 chance because he wants to entertain and build drama.

Just to see the answer is flawed use 4 boxes and take one and show one

Blue, Red, White and Yellow.

You take the white
He show's the yellow.

What's the probability for the Blue and Red and your white remember they have to add to 100%

1/4 that White contains gold
3/4 that Blue OR Red OR Yellow contain gold

Now he shows you Yellow does not contain gold.
White = 1/4
Yellow = 0/4
Blue OR Red = 3/4

... or in decimal numbers:

White = 0.25
Yellow = 0
Blue = ½*3/4 = 0.375
Red = ½*3/4 = 0.375

It does add up (0.25 + 0 + 0.375 + 0.375 = 1 = 100%), and it is stil better to switch

 

[bobhikes]

When you first choose the brown box, you have no knowledge of what is in either of the boxes, so the probability that the brown box contains gold is 1/3

The probability that the green OR the red box contains gold is 2/3.

He now shows you that the red box does not contain gold.
The probability that the green OR the red box contain gold is still 2/3, but since you now know for certain that thered box dos not contain gold...

Get it?

What I get is I'ld love to battle you with money and odds. If you think an equal choice between 2 boxes it is always better to take the other box, I can win an awful lot of money.

So your saying you don't have two senerio just one and the odds past freely between the two see example below and explain why it fails.

I gave you a choice of three boxes 1 with an apple and then opened 1 without an apple and instead of letting you pick between the two left over boxes substituted. Why should the odds change there are still two boxes and still two choices and one right answer.

Now one of the boxes contains an orange. Yours or the other what are the odds is it still 2/3.

 

[Kathryn]

The chances are the same for the brown box or the green box - the same as the chances were before one box was opened. The only difference now is that we know our chances are 50/50 instead of 1 out of 3.

Oh, and we'd be madder if we realized we had traded in the wrong box - maybe. If we were irrational.

There is no "what might have been." There is only "what is." We could drive ourselves crazy with "what might have been" scenarios in our lives, so I don't go there. It's pointless.

 

[Father Heathen]

Edit: :foot:

 

[lunamoth]

Lunakilo is correct: Monty Hall problem - Wikipedia, the free encyclopedia

Yay for Lunas!

 

[jarofthoughts]

Lunakilo is correct: Monty Hall problem - Wikipedia, the free encyclopedia

Yay for Lunas!

Indeed she is, and this riddle is, in fact, very old.
I'm sorry if it doesn't make sense to a lot of people, but mathematically changing to the green box is statistically the right thing to do.

 

[Father Heathen]

Sorry, Lunakilo, I stand corrected.

By switching, you only lose if you had picked the gold, which was a 1 in 3 chance.

 

[Penumbra]

This is, as previously mentioned, an old question, and sort of a trick question. (Not in the sense that there's actually a trick, but in the sense that it seems obvious, and yet the answer that most people give is wrong, including most smart people since they don't often take the time to analyze it.)

It's statistically preferable to switch to the green one, as long as is it phrased in the primary way rather than utilizing some of the variant rules of the game.

 

[Kathryn]

Well, I'm old and fairly well educated, and have never heard this riddle before. And to be honest, I still don't see how switching is the "right" answer statistically speaking. What does "phrasing it in the primary way" have to do with it. Sorry, but I don't even know what that means.

Obviously I am a pretty secure person to even outright ask these questions. This makes little sense to me. I don't see why I should switch choices - I simply do not see how that increases my odds of being correct. I mean REALLY increases my odds - not hypothetically increases my odds.

 

[Kathryn]

I fully understand the hypothetical concept of 1/3 and then 2/3 chances. But I'm not that interested in hypothetical concepts - reality is much more interesting.

I've read the Wiki article and some of the links. What I can't find is an actual study that verifies that switching increases the actual number of wins. I mean, I see suggestions (Try it with a deck of cards!) but I must be missing the actual STUDIES that prove that switching increases the number of wins. Not the ODDS - the WINS.

Surely I'm missing something here.

 

[Penumbra]

Well, I'm old and fairly well educated, and have never heard this riddle before. And to be honest, I still don't see how switching is the "right" answer statistically speaking. What does "phrasing it in the primary way" have to do with it. Sorry, but I don't even know what that means.

Phrasing can affect how the maths need to be done to show the result. Specifically, the instructions for which the host is supposed to operate are sometimes assumed differently. I don't know all variations, but the ones I'm familiar with all lead to the same answer.

Obviously I am a pretty secure person to even outright ask these questions. This makes little sense to me. I don't see why I should switch choices - I simply do not see how that increases my odds of being correct. I mean REALLY increases my odds - not hypothetically increases my odds.

Can you provide an example of something that hypothetically increases odds without really increasing odds? I don't know what that means.

I fully understand the hypothetical concept of 1/3 and then 2/3 chances. But I'm not that interested in hypothetical concepts - reality is much more interesting.

I've read the Wiki article and some of the links. What I can't find is an actual study that verifies that switching increases the actual number of wins. I mean, I see suggestions (Try it with a deck of cards!) but I must be missing the actual STUDIES that prove that switching increases the number of wins. Not the ODDS - the WINS.

Surely I'm missing something here.

If you're interested in the reality of winning, then it would be in your favor to switch. Mathematics are useless if they don't have applications- this one is applicable.

The math itself is rather straightforward once applied, but people still often don't believe it (it's rather unintuitive at first glance), so simulations can be run to show how you're better off switching.