As you may have seen, I put a video on YouTube about the question:



The Wizard has seen my video and I asked him if my video correctly shows the QUESTION being asked. He responded and I responded to the Wizard. Here it is from the WOV site:

Quote: Wizard
No, you didn't accurately depict the question. AT the 0:09 point you said, "If one of these two dice happens to show a two then our challenge is on." You never address what happens if BOTH dice are a two.


Actually, I think I did. Doesn't "if one of these two dice happens to show a two then our challenge is on" mean the same thing as:

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"Your partner peeks under the cup, and tells you, truthfully, "At least one of the dice is a 2."
What is the probability that both dice are showing a 2?
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You also raise the question "you never address what happens if BOTH dice are a two." Well, it doesn't matter. If both dice are a 2 then it is also a true statement that "at least one of the dice is a 2." And even if both dice show a 2, then in a 2-dice problem the answer still involves only 1 die.

And let me jump ahead: it doesn't matter which die shows a 2 or if both dice show a 2 in a two dice problem.

If die A shows the 2 then it's a question of what shows on the 6 sides of die B. If die B shows the 2 then it's a question of what shows on the six sides of die A.
And again, if both dice show a 2 then it's still a question of either die A or die B both of which have six sides.

And, to state the obvious: if the judge or partner peeked and didn't see "at least one of the dice is a 2" the "challenge" or "question" is no longer valid and the dice must be rolled again.

So, I think my video clearly illustrates the question, and explains the answer to the way the question was originally worded.

I want to add one more thing in case it somehow was missed: 1/11 is the correct answer to a different question. That question might be something like this: how many different combinations of two dice, with at least a 2 showing on at least one die, would show 2-2?" And here the answer would be 1/11 because there is only one 2-2 and 11 combinations of 2 dice showing at least one 2.

I've said it from the beginning: you have to interpret the language of the question. The language is specific.

Thanks.