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

[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.

[waryoptimism.livejournal.com]

As the question says, "What are the odds that the other die is also a six?"

So it's asking what the probability of getting (6,6) on two dice is; i.e. 1/36.

[theweaselking.livejournal.com]

Nope.

[waryoptimism.livejournal.com]

Ah, wait, it's the probability of 6 on 1 given 6 on 2. So P(6 on 1 and 6 on 2)/P(6 on 2), i.e.(1/6*1/6)/(1/6) or 1/6.

That better?

[theweaselking.livejournal.com]

No. It's the probability of at least one 6 on two dice.

[waryoptimism.livejournal.com]

Where A = a 6 on dice 1, and B = a 6 on dice 2, isn't the question the probability of B given A? That seems to be how it's worded.

[theweaselking.livejournal.com]

You've assumed that A must be a 6.

B could be a 6, and not A.

You're looking for A or B.

[stormfeather.livejournal.com]

Argh. Urgh. Hrm. Yeah, I answered 1/36 but looking back at the semantics, I guess it'd be... one in eleven?

[theweaselking.livejournal.com]

How do you reach this conclusion?

[stormfeather.livejournal.com]

Basically first read it as "what are the chances you roll two sixes" and figured out how many different rolls you could get on two dice (36) and went from there. Then after looking on here, I realized that I didn't quite get all the subtleties of the question right, and went back and figured out how many of those possible rolls would have a 6 in them, which is 11. (Two variations each for 7-11, then one for 12).

[anivair.livejournal.com]

... because you've already rolled one six. Odds go up.

[theweaselking.livejournal.com]

You rolled two dice. One of them *is* a six. What are the odds that the other is a six?

Without, I note, every knowing which of the two is the 6 in the first place.

[chaosrah.livejournal.com]

Oh. Alright. So one is a 6, but you don't know if the first one you rolled was the 6, or if it was the second one you rolled that was a 6.. so you still have to multiply 1/6 by 1/6. Chance of first one being a 6 is 1/6, then the second one must be a 6. Chance of second one being a 6 is 1/6, so the first must have been a 6. Blah blah. 1/36..

[theweaselking.livejournal.com]

Nope.

1/36 is the probability of *both* being 6.

You want the probability of *one or the other or both* being 6.

(Which is the same as 1 - (neither is 6))

[corruptedjasper.livejournal.com]

But just one of them being a six does not satisfy the requirements -- you basically get to 1/11, not 11/36.

[theweaselking.livejournal.com]

You're right, that was a stupid thing to say. It's one of the steps towards the solution, but it's missing the final step.

[cheshire-bitten.livejournal.com]

One of them is a 6.

What are the odds that the other<\b> is also a six?

That tells you which one is a six

[theweaselking.livejournal.com]

You don't know which is which. All you know is that one of them is a six.

[athelind.livejournal.com]

"The other" means "not that one".

[theweaselking.livejournal.com]

And which one is "that one"? One of the two. Which one? Puzzle doesn't say, so you don't know.

The puzzle is not ambiguous.

[publius1.livejournal.com]

I hate stupid questions like this. "How do you make 30 cents with a two coins, and one of them is not a nickel?" It's just dumb semantics, not a math question.

[scixual.livejournal.com]

Now you're adding things.

The question, as it stands, is,

One die is a six.
What are the odds the other is a six?

The first part is irrelevant.

The odds of rolling two sixes from the start is different. But the first die has nothing to do wit the second die.

Now, you're rephrasing it so it seems you've rolled two dice and don't know what either is, but you know at least one is a six. It's a different question.

I'm not actually sure of that one, I'll have to ponder it.

But as asked? The vast majority of your friends gt it right.

[theweaselking.livejournal.com]

Now you're adding things.

I am not.

The question, as it stands, is,

One die is a six.
What are the odds the other is a six?

It is, in fact, "You roll two fair 6-sided dice.

One of them is a 6.

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

The first part is irrelevant.

No, it is not. If I had started with "you roll 10 dice. One of them is a six. What are the odds that none of the rest are sixes?" would you say that this was the same as "the odds of no sixes on 9 dice?"

From the answers here, lots of people would. Those people would still all be wrong.

the first die has nothing to do wit the second die.

A true, but irrelevant statement.

Now, you're rephrasing it so it seems you've rolled two dice and don't know what either is, but you know at least one is a six. It's a different question.

It's the original question. You rolled two, one of them was a six. Which one? You don't know, because the question didn't tell you. One of the two dice you rolled was a 6.

I'm not actually sure of that one, I'll have to ponder it.

It's not a complicated question. There's only 36 results on 2d6 - a third-grader could brute-force the problem in 10 minutes.

But as asked? The vast majority of your friends gt it right.

No, they didn't. The vast majority taking the simple, intuitive, unambiguously wrong answer doesn't make it less wrong, or the question less clear. You rolled two dice, one of the two dice you rolled was a six - there is no ambiguity there. People who bring up "die rolls are independent" and "dice don't have a memory" and "the second die doesn't depend on the first" are all *correct*, technically, but none of those things change that the correct answer to this question is either 1/11 (probability) or 1:10 (odds), and that any answer of "1/6" is absolutely, completely, in every way, wrong.

Answering 1/6 shows that you didn't read the question.

[scixual.livejournal.com]

You didn't state the question as clearly as you think you did.

And stop being smug and superior about it, it's off-putting. Or ask a flipping third grader.