Let me just sum this up and return to the basic question. Just in case you missed the other threads this is the original "dice problem" as posted on the Wizard of Vegas message board:
You have two 6-sided dice in a cup. You shake the dice, and slam the cup down onto the table, hiding the result. 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?
There are two basic "sides" giving different answers: one side says the answer is 1/11 and one side says the answer is 1/6.
Video explanations for both sides have been presented.
In case you missed them, here they are again. First the video from Michael Shackleford who says the answer 1/11:
And here is my video and I say the answer is 1/6:
At first blush you can see a problem: Michael willingly "double counts" a die, but I don't. Both of us show at least one die rolled with a two and while I remove the die with a 2 to show the answer is 1/6, Michael keeps the die showing a 2 and "double counts" it to increase the number of options to be 11. Clearly he needs two dice to show 11.
I've asked this before and I am yet to get a straight answer: why are you allowed to "double count" a die in a two dice problem? I don't double count my die showing a 2 but Michael "double counts" his die showing a 2.
And so I need someone from the 1/11 "side" to clearly explain how they justify using one die "twice" to solve their problem? And explain why when the value of a die is known that they are allowed to change it?
The second conflict between the 1/11ers and 1/6ers is the interpretation of the original question (above, in bold).
I consider that question to be the same as this event and question at a craps table -- and this is an event that we've all seen a few times:
The shooter throws two dice and one die immediately comes to rest showing a "2" but the second die spins like a top. What are the odds that the second die will also come to rest showing a 2?
If you think this craps table event is the NOT THE SAME as the original question please explain why?
I added a poll reflecting these questions. Please participate.