The Wizard will bank this bet: 1/6 vs 1/11

[kewl]

The additional facts changed the odds. If the question was there is one die slammed down and the peeker said it was a 2, would you now say the odds that it is a 2 is 1 of 6??

No--it is a 2. 100%. No ifs ands or buts. The second die does not change anything. We have more facts than you are willing to acknowledge. The question is not what were the odds that that die would be a 2. The question relates to the 2 dice that were thrown this one time. We know what one of them is. We have only the other to consider and we all can agree on the odds for that one die.

Two dice make eleven combos representing 2-x, are they not?
So the odds for us to see 2-x are 11/36 are they not?
Now this above IS NOT IRRELEVANT to the odds of us seeing 2-2.
You 1/6ers are all claiming it is up to one die only, once we know there is a deuce among the two dice. It is not.

You have 36 cards (that's not for Alan - he disregards anything not involving dice for whatever reason) with every single combo of pair of dice on them.
Draw a card. Would you say now that the ways to draw one of those eleven 2-x are not influencing the odds of drawing the 2-2?

[redietz]

Kewl,

If you present a single event in present tense and then continue the narrative beyond it, usually the event is over, finished, not one of many events. Now the 1/11ers are arguing that using the word "probability" at the end in essence says that the author is expressly telling you that it was one of many events. The word "probability," however, does not have as its primary definition the mathematical definition they are trying to assign. So for their argument to make sense, they need both a non-conventional narrative structure and a secondary definition of "probability." It's possible, but convoluted, for a reader to interpret the piece of writing this way. It's probably more natural, common, call it what you will, for a reader to interpret it the way the "non-geniuses" interpret it. An editor would, after asking the author what the hell he really meant, completely rewrite the original question because of this.

[kewl]

That's the problem. You read books and misapplied what you learned. Now take a course in reasoning and another in reading comprehension.

No, I'm not misapplying anything. The bet you agreed represents the question straight as it was written and clarified, proves me right.

And indeed there is nothing much to say here. The odds are indeed 1/11. In the real, physical world they are. On a single throw. They are 1/11. Many times - still 1/11. In fact that's the ultimate proof. Many a times experimenting.

[kewl]

Kewl,

If you present a single event in present tense and then continue the narrative beyond it, usually the event is over, finished, not one of many events. Now the 1/11ers are arguing that using the word "probability" at the end in essence says that the author is expressly telling you that it was one of many events. The word "probability," however, does not have as its primary definition the mathematical definition they are trying to assign. So for their argument to make sense, they need both a non-conventional narrative structure and a secondary definition of "probability." It's possible, but convoluted, for a reader to interpret the piece of writing this way. It's probably more natural, common, call it what you will, for a reader to interpret it the way the "non-geniuses" interpret it. An editor would, after asking the author what the hell he really meant, completely rewrite the original question because of this.

It does not matter if we are talking single, one time throw or not. The odds are still the same.

[Alan Mendelson]

Two dice make eleven combos representing 2-x, are they not?

Why? Why do you persist in considering the various faces on both dice? When "at least one die" is identified as showing a 2, that die's other faces cannot be considered.

And by the way, this is the same problem with how the "textbook version" of the question is written. It is also poorly written, and should be changed. But, I understand how the "textbook version" will have the answer of 1/11 because it was written in the context of a probability lesson. Unfortunately, how it was written as part of a probability question is not good enough for a normal conversation. I realize you don't understand what I am saying or what redietz is saying or what regnis is saying about how sentences are written but we deal with "words" and you parrot math lessons. This is why I also wrote on the Wizard's forum that I wouldn't hire anyone for my company who says the answer is 1/11 -- I don't need that kind of overthinking of a basic problem.

[kewl]

Why? Why do you persist in considering the various faces on both dice? When "at least one die" is identified as showing a 2, that die's other faces cannot be considered.

Because they are related to everything, why can't you get it?

we deal with "words" and you parrot math lessons.

What's worse parrot or bigot not capable to comprehend neither math nor words?

Here is your one time throw example:

I, Bob, John and hundreds of 1/6ers would like to empirically proof the odds on question.
We decide we will only do the experiment once. But all of us will do it.
We throw dice. I got 6-4. Bummer. No question to ask, no answer, case closed.
Bob and 300 1/6ers got 2-x. guess how many of them got 2-2 and what the ratio tends to?
What does this tells us? Yeah, it tells us the real, physical world actually says the odds on getting 2-2 given at least one 2 are indeed 1/11. Damn...

[OneHitWonder]

Yeah, it tells us the real, physical world actually says the odds on getting 2-2 given at least one 2 are indeed 1/11. Damn...

No. Technically and simply, getting 2-2 given rolls of the set of at least one 2 is indeed a 1/11 chance. And then, if and only if a 2 is the explicit objective from the start. However, 1/6 is the answer which makes up the 1/11, no matter what. The 1/11 is a compound answer, ie, illusory in some way.

A specific roll which has or involves "at least one 2" doesn't include a non-2 with 2, or 2-2.

Damn! Better tell the Wizard. Lol.

[OneHitWonder]

A specific roll isn't a set of rolls, or the union of types of rolls. "At least one 2" refers to a set of rolls.

[kewl]

No. Technically and simply, getting 2-2 given rolls of the set of at least one 2 is indeed a 1/11 chance. And then, if and only if a 2 is the explicit objective from the start.

Well, that's one of the conditions as clarified like million times after the initial few posts on the old discussion. Have you missed it?

However, 1/6 is the answer which makes up the 1/11, no matter what. The 1/11 is a compound answer, ie, illusory in some way.

What's this nonsense?

]
A specific roll which has or involves "at least one 2" doesn't include a non-2 with 2, or 2-2.

Damn! Better tell the Wizard. Lol.

Wow, you're loosing it. Outright nonsense like this doesn't even deserve a reply.

"at least one 2" doesn't include a non-2 with 2, or 2-2.???????

I'll ignore all future nonsense like this on the spot.

[arcimede$]

Kewl if I used your question as a substitute for the original question I would say 1/6. But your new question is a textbook question that leads to the 1/11 answer.

The textbook question lacks the information given in the original question which is that the peeker sees at least one 2. That defines the original question as being a one time event.
You cannot apply your textbook methodology to this one time event in the original question.

Sorry, I'm smarter than you.

Doesn't matter if the throw in question is a "one time event". The question asks for "probability". Probability is calculated by considering all possible throws. What you are showing is you are not very smart..

[arcimede$]

Kewl,

If you present a single event in present tense and then continue the narrative beyond it, usually the event is over, finished, not one of many events. Now the 1/11ers are arguing that using the word "probability" at the end in essence says that the author is expressly telling you that it was one of many events. The word "probability," however, does not have as its primary definition the mathematical definition they are trying to assign. So for their argument to make sense, they need both a non-conventional narrative structure and a secondary definition of "probability." It's possible, but convoluted, for a reader to interpret the piece of writing this way. It's probably more natural, common, call it what you will, for a reader to interpret it the way the "non-geniuses" interpret it. An editor would, after asking the author what the hell he really meant, completely rewrite the original question because of this.

Good grief .... even when you answer the question with 1-6 you are giving a mathematical answer. That means you interpreted the question using the mathematical definition of probability. There is no definition of probability where 1-6 is the correct answer.

[arcimede$]

Why? Why do you persist in considering the various faces on both dice? When "at least one die" is identified as showing a 2, that die's other faces cannot be considered.

Look, everyone knows how you are failing to understand the question. Never is it stated that one particular die is a 2 and you can only look at the other die. It is stated that at least one die is a 2. It doesn't specify which one. Therefore, all combinations where either die could be the 2 must be considered to get the correct answer. Your continued denial of the obvious meaning of the question only makes it obvious you have become emotionally attached to the wrong answer.

[Alan Mendelson]

There's nothing emotional in what I am about to say: no one is presenting any new information here. On both sides.

[redietz]

Good grief .... even when you answer the question with 1-6 you are giving a mathematical answer. That means you interpreted the question using the mathematical definition of probability. There is no definition of probability where 1-6 is the correct answer.

Good grief yourself, Charlie Brown. If you find a quote where I said it was either 1/11 or 1/6, please let me know. I repeat my earlier example, "Arci winks at the cocktail waitress, slams down his drink, then peers down her blouse. What is the probability a sexfest ensues?" In your mind, is that a "math" question? And how is that clearly different from the original question in narration and what it is asking?

You say people need to learn to do math. Yeah, and people need to understand the difference between a sentence and an equation. What's most disturbing is that some people fail to understand that if a large chunk or majority of readers read something, and come to Answer A when the answer is B, then the problem lies with the author, not the readers. Arci, I hope you've tracked down the author and posted 50 times regarding what a lousy job he did. Just because you "got it" doesn't make it correct. You are not the arbiter of how people interpret pieces of writing and how they should interpret pieces of writing.

[kewl]

Good grief yourself, Charlie Brown. If you find a quote where I said it was either 1/11 or 1/6, please let me know. I repeat my earlier example, "Arci winks at the cocktail waitress, slams down his drink, then peers down her blouse. What is the probability a sexfest ensues?" In your mind, is that a "math" question? And how is that clearly different from the original question in narration and what it is asking?

You say people need to learn to do math. Yeah, and people need to understand the difference between a sentence and an equation. What's most disturbing is that some people fail to understand that if a large chunk or majority of readers read something, and come to Answer A when the answer is B, then the problem lies with the author, not the readers. Arci, I hope you've tracked down the author and posted 50 times regarding what a lousy job he did. Just because you "got it" doesn't make it correct. You are not the arbiter of how people interpret pieces of writing and how they should interpret pieces of writing.

But it doesn't matter how is this question interpreted regarding one time action or multiple experiments. The odds hold true every single time and it is not 1/6, so why are people blaming the writing?
One ambiguity there is and it is regarding the peeker intention to announce whatever value is there or specifically a deuce and it was cleared for the purpose of this discussion long time ago.

[kewl]

There's nothing emotional in what I am about to say: no one is presenting any new information here. On both sides.

Not quite sure about that.
It seems it is new information for you that whether you do a one time experiment or multiple times doesn't matter and the odds are still the same.

It is quite new info for you again, that the number of ways to get 2-x actually influences the odds on getting 2-2. only if you could educate yourself enough to see why. I'm afraid I'm running out of examples and ways to describe the why in simple logical terms and you seem to be unwilling to learn anyhow.

[OneHitWonder]

"At least one 2" doesn't include a non-2 with 2, or 2-2.???????

A specific roll which is (an element) of a defined set of rolls is different from a roll which is a defined set of rolls. A major difference, but one which may seem an unobvious nuance to someone with virtually no algebraic experience.

The problem as written here doesn't address a specific roll which "is (an element) of" a set of rolls. It addresses the specific roll as, "At least one of the dice is a 2." It does not mention the words "is (an element) of" the "at least one of the dice is a 2" set of rolls of the 1/11 chance answer.

The roll in the problem by which "at least one of the dice is a 2" means a roll by which one or two of the dice is a 2. This definitely doesn't include a non-2 with a 2, or 2-2. Eg, an end roll of 6-2 isn't included in one or two of the dice is a 2, because 6-2 has no possibility of two of the dice is a 2. However, a specific roll of 2-X, where X has yet to be determined, has the possibility of one or two of the dice is a 2.

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?

The set of rolls defined by "at least one 2" definitely does include {a non-2 with 2} or {2-2} but is different from a specific roll defined by "at least one 2". The latter doesn't include a non-2 with 2, or 2-2. It's the set of rolls of 2-X, where the X-die has yet to be looked at: {2-(1), 2-(2), 2-(3), 2-(4), 2-(5), and 2-(6)}. An end roll of this set is either 2-1, 2-2, 2-3, 2-4, 2-5, or 2-6.

Wow, you're loosing it. Outright nonsense like this doesn't even deserve a reply.

You apply the nonsense word as "a crutch" to not make the effort to understand what I and others have written, and then to not write an intelligent reply. Even a nonsense idea deserves an intelligent reply, as I continue to reply to you.

In my opinion, this is, foremost, a math question. Not a gambling forum, or court of law, exercise. To this end, I will post it up at one of the math forums, along with a summary of my own arguments of course, when I have some more free time.

It doesn't surprise me that neither the Wizard nor Alan has chosen such a form of "binding arbitration". They aren't the math and formal logic experts. Aside from redietz, and perhaps Singer, I get the feeling that a lot of this went over everyone's head. Same at the Wizard's.

[OneHitWonder]

One ambiguity there is and it is regarding the peeker intention to announce whatever value is there or specifically a deuce and it was cleared for the purpose of this discussion long time ago.

Not by the original problem. That's the problem the Wizard replied to immediately, and the one at hand here. Calculations and simulations are a distant second.

[Alan Mendelson]

Let me ask the question differently: if instead of using the word probability and we used the phrase "what are the chances that the other die is also a 2" would the 1/11 answer still hold?

[OneHitWonder]

Probability is the math word for chance. Like faith is the religious word for trust.