Originally Posted by a2a3dseddie View Post
So what reduces the 1/11 scenario you describe here to 1/6 after you put both dice both in a cup, roll them simultaneously, and a peeker says at least one of the dice is a 2?
I am glad you wrote this, because this illustrates the problem: they are different questions, and because they are different questions they have different answers.

I've been telling you this all along. You get 1/11 as the answer to one question, and you get 1/6 as the answer to another question. What you are doing is confusing the questions because you are missing the language of the questions.

redietz accurately pointed out that to answer the question about the dice in the cup with the peeker you would look at the dice one at a time (successive observation, not simultaneous observations) and that would give you the answer of 1/6. But when you are able to consider both dice at once (simultaneous observation) AS IF YOU ARE LOOKING AT A CHART OR A GRAPHIC OF DICE RESULTS your answer can be 1/11.

You are failing to recognize the wording and the condition of the question that gives you the answer 1/6. For some reason you are mistaking the question and applying the method that gives you the 1/11 answer.

Once again it's a problem of reading comprehension and it's a problem of not answering the question that is being asked.

These are all valid answers: 1/36, 10/36, 1/11, 1/6, 0/36 -- but they are not the correct answers to all questions.

1/36 the chance of rolling 2-2
10/36 the number of combinations of dice showing one 2
1/11 the number of combinations of dice showing at least one 2 that has 2-2
1/6 the face on one die that will match the face of another die
0/36 when you roll two dice but fail to get the combination you want

So, once again, when do we properly get the answer 1/6 ?? We get the answer 1/6 when we are asking how many faces on a die would match the face of a certain die. So, when we are told at least one die is showing a 2, there is 1/6 faces on a die that would have us have 2-2.

I'll say it again in a slightly different way:

If we are told that at least one die is showing a 2, to get a combination of 2-2 we would know that 1/6 faces on another die would present that.

In the dice in cup with peeker problem it is clearly said that at least one die is a 2.
When we look at a chart or graph or dice combinations we can see that 11 combinations have at least one 2 and one combination has 2-2.
When we are told that at least one of two dice is showing a 2 we don't consider 11 combinations-- we only consider what are the possible combinations of the second die in the problem.

Why can't you understand this?