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.
(no subject)
Date: 2011-08-19 12:09 pm (UTC)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.