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AlanMendelson
AlanMendelson 
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May 10th, 2022 at 5:19:02 PM permalink
Quote: Wizard

Quote: AlanMendelson

...For everyone here's the original wording:

_____________________

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?
_______________________

And here's the problem with the wording. It is in this sentence.

"Your partner peeks under the cup, and tells you, truthfully, 'At least one of the dice is a 2.' "

The question is phrased in such a way that it makes you take on the role of "the partner" who looks under the cup.



What are you talking about? The question states the partner is a separate person. You are not the one peeking under the cup.

Quote:

Now, as "the partner" what do YOU see when you look under the cup?



The question doesn't state that, except that he either sees one or two two's.

Quote:

As I wrote when this problem was first presented, I suggested a PROPERLY PHRASED question would be something like...

How many combinations of two dice show at least one 2, and how many of those combinations would be 2-2?



That is a very simplified version of the problem. The goal of the original wording was to get from that wording to how you stated it, or to solve it some other correct way, like Bayesian analysis.

Quote:

Instead, we got an awkwardly written question which elicits a different answer than what was intended.

As I pointed out before... it's not a math problem, it's an English problem. And unfortunately the bad English has been repeated so many times it has become accepted.



There was nothing wrong with the original wording. You just didn't understand it.

Quote:

But if you take the position of the partner who peeks under the cup, like the partner who sees one die showing a 2 you would have to say the answer is 1 out of 6.



No!!!!!!!!! The question never said you are the peeker and see just one die.

Quote:

Of course I mentioned this before and I was told I dont understand English. So, I give up.
link to original post



That's right -- You don't understand English. Your interpretation of the problem is completely ridiculous. I admit your spelling and grammar are fine, but your reading comprehension about this and everything related to math is terrible.

If you feel this is an insult, report it, I'll accept the punishment of any other moderator. However, I had to get that off my chest.
link to original post



I have nothing more to say. We disagree.
OnceDear
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OnceDear 
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Thanks for this post from:
BleedingChipsSlowly
May 11th, 2022 at 10:32:09 AM permalink
Quote: Wizard

Quote: AlanMendelson

I have been accused of being a math denier only for saying what I've seen. And not because I ever challenged any math.
link to original post



You absolutely are a math denier. That is crystal clear from your hundreds and hundreds of posts in denial of the answer to the two-dice problem.

If this were an astronomy forum, you would be the one proclaiming the earth is flat.
link to original post


Wizard,
TLDR Three days posting suspension. You may still moderate spam etc, but for any judgement calls, I ASK that you get approval after any action from one of we three other moderators.

Wizard is NOT being penalised for this...
Quote: wizard

That's right -- You don't understand English. Your interpretation of the problem is completely ridiculous. I admit your spelling and grammar are fine, but your reading comprehension about this and everything related to math is terrible.

If you feel this is an insult, report it, I'll accept the punishment of any other moderator. However, I had to get that off my chest.


He IS being penalised for this...
Quote: wizard

If this were an astronomy forum, you would be the one proclaiming the earth is flat.




Unfortunately, there is no penalty under the rules for engaging Mr Mendelson on the question which he cannot comprehend. There should be. He does not understand the question, He cannot understand the question and he will not understand the question. Maybe that makes him a math denier, or maybe he is just hard wired to not comprehend statements of logic. Attack his logic, his maths or his comprehension, but don't attack HIM.

Accusing him of being a math denier is harsh but understandable and somewhat underscored by evidence. Accusing him of being a Flat Earther, in the absence of evidence, is a personal insult. I suggest a penalty, whereby you suspend yourself for three days while you re-read the entire two dice thread, part one and two.
Incidentally, the correct answer to the original question as posed can, of course be "one in six", but not under the conditions that AM suggests. It only needs for the calling rule to be that when the peeker looks at the dice and they are of values X and Y, that he truthfully declares that 'At least one of the dice is a 'Y'' THE CALLING RULES WERE NEVER GIVEN! Only the observation of one calling event.
I.e. In the scenario observed, one dice was a two. If the dice had shown 2 and 4, he MIGHT have truthfully declared "At least one of the dice is a 4" It would have been true.
Heck, the calling rule MIGHT have been "If only one of the dice is a two, I will call "At least one of the dice is a two, but if both of the dice are two, i will call "Both of the dice are twos"

And on that note. I return to my therapist!!!!
Last edited by: OnceDear on May 11, 2022
Beware. The earth is NOT flat. Hit and run is not a winning strategy: Pressing into trends IS not a winning strategy: Progressives are not a winning strategy: Don't Buy It! .Don't even take it for free.
OnceDear
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OnceDear 
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May 13th, 2022 at 10:45:55 AM permalink
During Wizard's current short suspension, I've been debating with him by PM $:o)

I think, now feel sure that, I annoyed him by reawakening the nightmare that we all argued so much.
Well, Wizard, You started this thread. LOL. You also suggested I bring my argument here!

Wizard: I respect you sir. I'm your subordinate here. This post is for the amusement of the forum and for the furtherance of Maths and logic. Wizard should be able to whup my ass on logic and maths.... Well if he were not currently indisposed.

I have requested that he permit me to refer to that PM exchange in thread, because frankly I think it has entertainment value. He did suggest it early in our discussion. So, I believe that it is acceptable under the rules for me to quote a small snippet of my outgoing PM to him....

Quote: Me to Wizard by PM


Now..... You may challenge my assertion that 1 in 6 is A CORRECT answer to the question as posed, by PM even while suspended.



Red rag to a bull. LOL. He thought I was joking with my 1/6 assertion.
He might have been irritated when I suspended him, too.

Now, to those who are new to the forum, the original 'Two Dice Puzzle' Thread was massively popular and controversial. It ran through 2013 to 2015 over many hundreds of posts and the arguing went on over more than two years. It spilled out to other forums and various high flying consultants were pestered.

Moderators had nightmares over it and this one almost needed therapy $;o)

And Wizard referenced it again, thus 'yanking my chain'

To summarize the controversy
The answer to the posed question as asserted by Wizard was, and still is 1/11. He is adamant.
The answer, as insisted upon by many, was 1/6. Alan Mendelson was a particular advocate of that answer.
The answer proposed by some, including myself was 'Indeterminate because we have to make assumptions'. I stand by my answer

Oh boy. I hope he doesn't take offence at my arguing with him. As per the rules, I'm not attacking him, just countering his argument. A lot of this is about semantics. Not as much fun as Math or logic.

Note. In spite of my answer of potentially 1/6. I do NOT support Alan M's arguments as to why it is potentially 1/6

I'll leave it there until Wizard returns, because it would feel unfair to challenge his logic here while he is suspended.
Beware. The earth is NOT flat. Hit and run is not a winning strategy: Pressing into trends IS not a winning strategy: Progressives are not a winning strategy: Don't Buy It! .Don't even take it for free.
gordonm888
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gordonm888
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May 13th, 2022 at 11:05:06 AM permalink
Quote: OnceDear

During Wizard's current short suspension, I've been debating with him by PM $:o)

I think, now feel sure that, I annoyed him by reawakening the nightmare that we all argued so much.
Well, Wizard, You started this thread. LOL. You also suggested I bring my argument here!

Wizard: I respect you sir. I'm your subordinate here. This post is for the amusement of the forum and for the furtherance of Maths and logic. Wizard should be able to whup my ass on logic and maths.... Well if he were not currently indisposed.

I have requested that he permit me to refer to that PM exchange in thread, because frankly I think it has entertainment value. He did suggest it early in our discussion. So, I believe that it is acceptable under the rules for me to quote a small snippet of my outgoing PM to him....

Quote: Me to Wizard by PM


Now..... You may challenge my assertion that 1 in 6 is A CORRECT answer to the question as posed, by PM even while suspended.



Red rag to a bull. LOL. He thought I was joking with my 1/6 assertion.
He might have been irritated when I suspended him, too.

Now, to those who are new to the forum, the original 'Two Dice Puzzle' Thread was massively popular and controversial. It ran through 2013 to 2015 over many hundreds of posts and the arguing went on over more than two years. It spilled out to other forums and various high flying consultants were pestered.

Moderators had nightmares over it and this one almost needed therapy $;o)

And Wizard referenced it again, thus 'yanking my chain'

To summarize the controversy
The answer to the posed question as asserted by Wizard was, and still is 1/11. He is adamant.
The answer, as insisted upon by many, was 1/6. Alan Mendelson was a particular advocate of that answer.
The answer proposed by some, including myself was 'Indeterminate because we have to make assumptions'. I stand by my answer

Oh boy. I hope he doesn't take offence at my arguing with him. As per the rules, I'm not attacking him, just countering his argument. A lot of this is about semantics. Not as much fun as Math or logic.

Note. In spite of my answer of potentially 1/6. I do NOT support Alan M's arguments as to why it is potentially 1/6

I'll leave it there until Wizard returns, because it would feel unfair to challenge his logic here while he is suspended.
link to original post



I do agree with Wizard. In my opinion, the answer to the posed question is 1/11.
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
DJTeddyBear
DJTeddyBear
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May 13th, 2022 at 11:33:22 AM permalink
That original thread got started in October, 2013!

I also agree that the odds are 1/11. I知 sure my rationale is already posted in that thread, or in the part deux thread, so I won稚 duplicate my reasons.


Quote: Wizard

If this were an astronomy forum, you would be the one proclaiming the earth is flat.
link to original post

Nah. He壇 incorrectly proclaim that the earth is round. 😵‍💫
I invented a few casino games. Info: http://www.DaveMillerGaming.com/ 覧覧覧覧覧覧覧覧覧覧覧覧覧覧覧覧覧覧 Superstitions are silly, childish, irrational rituals, born out of fear of the unknown. But how much does it cost to knock on wood? 😁
billryan
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May 13th, 2022 at 11:49:03 AM permalink
Can someone walk me thru this?
The difference between fiction and reality is that fiction is supposed to make sense.
Dieter
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May 13th, 2022 at 12:04:14 PM permalink
Quote: billryan

Can someone walk me thru this?
link to original post



Please tell me you're asking about dice and not Ball Eartherism.
May the cards fall in your favor.
gordonm888
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May 13th, 2022 at 12:44:44 PM permalink
Quote: billryan

Can someone walk me thru this?
link to original post



Your friend looks at the two dice and truthfully reports to you that "at least one of the two dice is a 2."

Now if the dice had been colored red and blue, and your friend had reported to you that the red die was a 2, then the probability of the blue die being a two would be 1 in 6. That's common sense. And the people arguing for 1 in 6 seem to be applying this common-sense conclusion to the problem.

But the friend has reported that "at least one of the two dice is a two." So, it's a different problem statement and you need to return to the original probabilities of the dice rolls.

1 and 2 2/36
2 and 2 1/36
3 and 2 2/36
4 and 2 2/36
5 and 2 2/36
6 and 2 2/36.

Those are the only dice roll outcomes that count because you have been informed that at least one of the dice is a 2 which corresponds to 11 of the 36 possible original dice roll outcomes.

And rolling a pair of 2's has a probability weight of 1 out of 11 for those dice roll outcomes.
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
billryan
billryan 
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May 13th, 2022 at 12:58:16 PM permalink
I appreciate the explanation and accept it, but don't fully grasp it.
The difference between fiction and reality is that fiction is supposed to make sense.
AlanMendelson
AlanMendelson 
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May 13th, 2022 at 1:03:06 PM permalink
Billy...

Suppose I told you I had two dice in a cup. After shaking I told you at least one of the dice is a 2.
Then I asked you, what are the odds that the other die is also a 2?

What would you say?

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