# Which box should you open?

Asked by flutherother (30682) August 21st, 2010

There are three boxes, two contain cabbages and one contains an expensive diamond. You select one box at random as the boxes appear identical. Your quizmaster opens one of the boxes you didn’t choose to reveal a cabbage. What should you do, stick with your first choice or choose the other unopened box?

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Open the other box. I have no idea why – I just remember my old maths teacher once asking us an identical question.

You should always switch ;) A lovely friend of mine is a math major, though she told this riddle using goats and not cabbage.

muppetish (14211)

Curious. There is a one in three chance of the diamond being in any particular box. Why should you imagine that changing your mind will improve your chances?

flutherother (30682)

I like cabbage and diamonds… so I would open the one on the left

talljasperman (21866)

It’s the Monty Hall paradox: you begin with a one in three chance. When one of the boxes is opened and proven to be nothing but cabbage, one naturally thinks, “Well, there are only two left – I have a fifty/fifty shot at being correct; I’ll just stick with my box.” But if they were to switch, they would actually have a ⅔ chance.

Of course, that sucks the fun out of riddles, so, um… “When is a door not a door?”

muppetish (14211)

@flutherother, you’re in good company: the great Hungarian mathematician Paul ErdÅ‘s also got it wrong, and was said to be very difficult to convince what the right answer is. See the Wikipedia article that @muppetish links to.

The catch in logic is that the emcee knows which door has the prize—he has more information than you do. His opening a door is not an independent event.

gasman (11315)

I would’ve stayed with my first choice being it wouldn’t matter to me if I was never told I could keep it.
If I am given the choice of choosing 2 out of 3 than my chances are 66 % but, if I have to remain with just the one than my chances go down to 33 percent chance of getting it right. I would think that after the extra cabbage is revealed and out of the equation than I drop from 66% to 50% or what is remaining unrevealed.

Pandora (29733)

I would sniff all 3 boxes. ;-)

@muppetish When it’s a jar.

LuckyGuy (39101)

@worriedguy Thank you for humouring me :) I love that riddle more than I probably should.

muppetish (14211)

Do not switch, stick with it. They would be expecting you to switch.

@muppetish That is one of the first riddles I ever learned. I still think it when I see the “Door Ajar” message on my car dashboard display.

LuckyGuy (39101)