Because MATH, that's why.

[theweaselking]

You roll two fair 6-sided dice.

One of them is a 6.

What are the odds that the other is also a six?

[Poll #1770498]

Comments

[tsunami-ryuu.livejournal.com]

Ahhh, tricksy question. I answered incorrectly because I didn't think that one through. It's all in the wording.

[theweaselking.livejournal.com]

You can re-answer by clicking the poll number and clicking "Fill Out Poll"

[theweaselking.livejournal.com]

Seriously, people?

[chaosrah.livejournal.com]

If you already rolled one die, then the second die is independent of the first. 1/6, right? I mean, if you rolled two die and said what are the chances they are both 6s, that's 6x6, 1/36. I know I'm not good at math, but I remember these tricky things in school.. If I'm wrong, I need an explanation.

[brerandalopex.livejournal.com]

The odds/probability are actually rather meaningless without a point of reference or some goal in mind.

If six was the desired number from the outset, then the chances of having one die come up six and the other also come up six after a single roll is 1/36, regardless of whether you told me that one of them was a six before revealing the results. True, there is an 11/36 chance that one is a six, and then you get to ask your clever question, but that doesn't change the outcome of the original roll or the probability of achieving double-sixes.

If there is no goal from the start, I roll two die, and you are required to reveal to me what one of the die's value is, then the probability that the other is the same value is the probability of rolling a pair of any sort, which is 1/6. Unlike the first scenario, you always get to say something, and your question is always a cleverly-disguised way of asking what the chances are that I rolled a pair.

Sure, there are 11 ways in which you can have two die with at least one 6, but only one of those in which both are 6, but I can't imagine any scenario in which this actually translates to meaningful odds/probabilities. Can you describe a game or contest like the Monty Hall scenario in which the 1/11 probability actually comes into play? Otherwise it sounds like you're throwing around numbers that have no real-world analog or application.

[dianavilliers.livejournal.com]

1/11.

[theweaselking.livejournal.com]

How do you reach this conclusion?

[cacahuate.livejournal.com]

Agreed, I think. Or if we’re being picky about odds vs. probability, the *odds* are 1 to 10.

[ciphergoth.livejournal.com]

This was my conclusion also. Of course a lot can turn on the wording of the question. I read it as "You roll two die over and over until you get a six. What are the odds that it's a double six?"

[silmaril.livejournal.com]

1/11.

(This is how tired I am: I had to actually write out the complete set, delete everything that didn't have a six in it, and count. I was left with {(6,1),(6,2),(6,3),(6,4),(6,5),(1,6),(2,6),(3,6),(4,6),(5,6),(6,6)}, which I rewrote here and recounted just to make sure my count was right. I think if you were to pull out the flaying knives now I might be able to do the formal derivation, but not otherwise. Tiiiiiiired.)

[silmaril.livejournal.com]

(Also, I completely approve of both your choice of title for the post, and now that I have skimmed up, dianavilliers' choice of method of illustration.)

[a1057soul.livejournal.com]

depending on how you read the question... there are 11/36 possible combinations where a 6 is present: 1-5,6 and 6,1-6.

The question asks if one of the die is a 6 and what is the probability that the other is ALSO a six... this to me indicates BOTH sixes, which has a probability of 1/36 based on each having 6 outcomes on two dies... assuming of course 'fair sided' means numbering from 1-6 (this isn't stated).

The probability of rolling a 2nd six after identifying the first is 1/6, but the probability of rolling 2 sixes is 1/36.

But then I generally do my math like this (http://www.giantitp.com/comics/oots0034.html).

:o.
Dan

[theweaselking.livejournal.com]

No, the question states that one of the two is a 6, without ever saying which.

And yes, I know Durkon. He's several close personal friends.

[crazy-alexy.livejournal.com]

This shit is why I hate math. -.-

[theweaselking.livejournal.com]

There's only 36 possible answers! brute-force exhaust it!

[ipslore.livejournal.com]

Okay, there's four possibilities:
1) *The one that's a six is a six, and the other one is a six
2) *The one that's a six is a six, and the other one is not a six
3) *The one that's a six is not a six, and the other one is a six
4) *The one that's a six is not a six, and the other one is not a six.

Clearly, we can eliminate 3) and 4). That leaves us with a 1 in 6 probability that the die other than the die that's a six is also a six.

(alternate, smart-ass answer: the odds are 0, because 'one of them' means 'exactly one of them'.)

[theweaselking.livejournal.com]

No, and no.

[kafziel.livejournal.com]

Without reading other comments: is it 1/11?

[dreamshade.livejournal.com]

Bah, I understood the general idea because I'd already heard the "one of my children is a boy, what are the chances that the other is" puzzle, but then I went and read the comments before doing the exact math and spoiled it for myself.

[dscotton.livejournal.com]

I got 1/11. 11/36 die combinations include a six. 1 of those consists of two sixes.

[krinndnz.livejournal.com]

Yes, questions are harder to answer when they're worded badly. Every time you post this (e.g. the raptors) I think you're an asshole.

[pappy-legba.livejournal.com]

Livejournaler confuses poor wording for cleverness, film at 11.

[ciphergoth.livejournal.com]

http://xkcd.com/169/

[ali-in-london.livejournal.com]

[x] Some initial answer, but then reading the comments convinced me I was wrong.

[tempter.livejournal.com]

I'm curious what you think the answer is.

[theweaselking.livejournal.com]

It's 1/11.

You have rolled two dice. One of them is a six, meaning you have 11 possible combinations. Of those 11, one has two sixes.

[fridgepunk.livejournal.com]

1/6 because the die that came up six is loaded and always comes up 6.

Problem?

[theweaselking.livejournal.com]

This is like the "100%, because I am actually Agent Michael Scarn of the FBI, and I have a gun!", right?

[heavenscalyx.livejournal.com]

More evidence that I still have PTSD and memory gaps from my horrible required statistics course 20 years ago.

[thornae.livejournal.com]

If I'm rolling them? 1.


(Actually, I made the same table as dianavilliers in my head, and got the same answer. But I've been watching a lot of The Mentalist lately...)

[cavalorn.livejournal.com]

Kicking myself now for misreading the question.

I'd seen it as an issue of 'two dice rolled under separate cups - you look at one of them, see it is a six, and therefore the die under the other cup has a one in six chance of being a six.'

But that's not the question you were asking at all, I see.

In fact, it's much more like this:

Your GM rolls 2d6 behind his GM's screen. He looks at them and says 'Well, one of these is a 6.' You then have to figure out the odds of the other one being a 6 too.

[littlebus.livejournal.com]

The question is too ambiguously worded to be a useful probability question, but is a good semantics riddle.