Two Dice Puzzle: Part Deux

Quote: Wizard

What happened to all the camp 1/6 members? Is there a Flat Earth Society meeting keeping them busy?

Coincidentally, I was just informed that I made a conditional probability error where the correct answer was 1/6. I originally had 1/5. How many push ups do I own for that one?

Quote: miplet

Coincidentally, I was just informed that I made a conditional probability error where the correct answer was 1/6. I originally had 1/5. How many push ups do I own for that one?

25 -- To be done at the next WoV gathering.

Quote: Wizard

I am looking forward to Alan personally getting in touch with me to resolve or concede the bet. He may get an F in probability but he is an honest man in my eyes until proven otherwise.

For everyone to see:

Yes, Wizard, I will probably lose the bet. But on my next visit to Vegas I would like to go through the motions of it anyway (for the fun of it) and then I would be more than pleased to buy you lunch.

Regarding the discussion: on my forum several mathematicians including a professor who is with some mathematics group joined the discussion and as they dissected the wording of the question, they conceded the correct answer is 1/6.

And then the discussion died off.

You can see the end of the discussion here: http://forum.alanbestbuys.com/showthread.php?3454-The-Wizard-will-bank-this-bet-1-6-vs-1-11/page41 starting with post #805 by onyx99 followed by post #818 by jihkro who said he was a professor and with http://math.stackexchange.com/

The wording of the original question, as the 1/6 supporters interpret it, must keep one die fixed on 2. It would be the same as rolling one die that comes to rest on a 2 and then rolling a second die. However, that is not what happens when two dice are rolled simultaneously by hand or from a cup which is the 1/11 result.

Quote: AlanMendelson

The wording of the original question, as the 1/6 supporters interpret it, must keep one die fixed on 2. It would be the same as rolling one die that comes to rest on a 2 and then rolling a second die. However, that is not what happens when two dice are rolled simultaneously by hand or from a cup which is the 1/11 result.

The latter is how I interpreted the wording of the question that you posted. It's clearly simultaneous:

"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?"

I don't see how you can misinterpret that as being equivalent to "rolling one die that comes to rest on a 2 and then rolling a second die."

Quote: AlanMendelson

For everyone to see:
....
However, that is not what happens when two dice are rolled simultaneously by hand or from a cup which is the 1/11 result.

Alan,
Just in the interest of clarity.

Are you now agreeing that in the wager as agreed with Mike, that a single deuce would be the result ten times more often than a pair of deuces? ... and certainly not five times more often, on average of course.

Are you further agreeing, by implication, that your agreed wager does not accurately reflect your own interpretation of the original question?

... And are you also agreeing that Mike's offer to pay less than 10:1 would put him at a statistical, mathematical, real world advantage, over a significant number of rolls, setting aside that 'anything can happen with rolling dice just a small number of times'?

Oh boy. Here we go again. Spiraling into the abyss.

Sorry to wake up what is one of the most dreadful threads on this site, but I have been meaning to redo my video in which I attempt to explain the answer "using only dice." My first video had a comment about double counting that I think confused the audience and I've been meaning to redo it ever since. I finally got around to it, at the same time I did the commentaries on the video poker challenge. Here it is. I welcome all comments.



Here is the original video. Question for the forum -- should I remove the original video or keep it up?

Keep it, both are simple explanations, thanks
Kind regards

Quote: beachmonkey

Keep it, both are simple explanations, thanks

Thank you and you're welcome!

Quote: Wizard

Sorry to wake up what is one of the most dreadful threads on this site, but ...

Ggaaaarrrhhhhhh. Ya b*****. Years of therapy undone.
Not forgiven.