Your answer is indeed 1/6. I absolutely agree that your answer is 1/6. You don't seem to like it when I agree with you.Quote:
Originally Posted by Alan Mendelson
Your answer is still wrong though. That seems to be one thing we will never agree on.
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Your answer is indeed 1/6. I absolutely agree that your answer is 1/6. You don't seem to like it when I agree with you.Quote:
Originally Posted by Alan Mendelson
Your answer is still wrong though. That seems to be one thing we will never agree on.
Just as expected, these WoV theorists couldn't spin the problem enuf to get common sense based people to fall for their BS, so they've returned to wizard's jumping up & down like crying kids because they couldn't convert people with more brains than them, and namecalling those over here. All with anonymous courage. But I understand their frustration with me at least, after I humiliated wizard, math extremist, and several other mensas in the past when they were afraid to meet up with me in LV and wanted no part of betting me that my play strategy would win as they watched--of course, after bravely claiming that I was a "fraud". Their method then? Ban me :)
So Alan, being that those clowns actually gave us the ultimate compliment by running away like sissies, job well done!
Like I said, the last time I saw this approach at reasoning it was by con artists who went to prison.
Once again state your case. Skip the questions. No demonstration needed.
Who ran away? I'm still here. I'm somewhat bored trying to get Alan to see sense. Alan has given up, not I.Quote:
Originally Posted by Rob.Singer
You, Rob, you don't even rise to the challenge to your own untenable standpoint. You just ignore it or describe it in BS words like 'wordsmithing'. I'm trying to figure out who is doing the namecalling? Other forum members can make their own judgements.
Alan,
Third time lucky. I asked...
Quote:
Originally Posted by OnceDear
Once Dear you owe me an apology. I am traveling and responding to the forum using my smartphone. Excel is not available. Be sure you mention this on the Wizard's site as well.
Basic conditional probability:Quote:
Originally Posted by Alan Mendelson
The probability of A given B = Probability of (A and B are true)/Probability(B is true)
In this case, A = "The dice show 2-2"
B = "At least one of the dice shows 2"
The fact that at least one of the dice shows 2 is a necessary condition for both dice to show 2, so Probability(A and B are true) is the same as Probability(A is true)
Therefore,
The probability of The dice showing 2-2 given that at least one of the dice shows 2 = (Probability of dice showing 2-2)/(Probability of at least one die showing 2).
There is 1 way, with probability of 1/36 to roll two dice so that they show 2-2. There are 11 ways, with probability of 11/36 to roll two dice so that at least one die shows 2.
(1/36)/(11/36) = 1/11, the probability that two dice show 2, given that at least one of them shows a 2.
Well Alan, I showed you how to solve this problem back on page 1 with two coins. The math steps are exactly the same. Now, all the possible throws are given to you and yet you still are in denial.
Look, it all gets down to how the question is asked. You refuse to accept there are two ways of phrasing the problem. Once you accept there are two different questions then maybe you will realize each question has a different answer.
PS. Did you note the last post from Singer is full of name calling and lies? Did you really expect him to change?
Arc there is only one answer for the one way the question was asked. I'm afraid the 1/11 crowd has been trying to change the question or they read it wrong. I said this early on. As the question appears and was originally stated the answer is 1/6. Even Once Dear concedes this conditionally.
As I said earlier, it's bad writing that creates the pseudo-paradox. If these folks wanted to be clear, they could be clear. They're interested in being oh-so-clever, not clear.
As for wordsmith being a BS word, as OnceDear suggested, I'm going to point out that it's a very interesting word in that it has an established definition (someone who is expert at using words; a professional writer) and an urban moderne usage, namely one who strings words together in pleasing, interesting, amusing ways regardless of their meaning. I'm not sure which definition Rob was using.
For what do I owe you an apology, this comment?Quote:
Originally Posted by Alan Mendelson
Well. I did find it funny. That is my privilege. I did not misquote or misrepresent you. You had previously mentioned that you would fire someone who disagreed with you on this 1/6 1/11 issue. That's not a direct quote, but a parody based on your previous style of posting.Quote:
The funniest so far, has to be Alan announcing on his forum (about a fellow member's independent proof)...
"Synergistic your application of Excel was just wrong."
Closely followed by
"Sorry, I am not using a regular computer and I am unable to see the spreadsheets. "
And this guy claims to be a business man. What did he do? Fire the cretin that suggested using a spreadsheet application?
And as to 'And this guy claims to be a business man' Well that came from my incredulity that wherever you are and whatever you are using to reply to forum posts with, I would have found it strikingly unusual to not have access to a laptop with Excel.
If you are offended by the tone of my posts, then be assured that no personal offense was meant. If I owe you an apology for any factual misrepresentation, anywhere, then direct me to that misrepresentation and I will happily put that right with appropriate humility.
I might have a personal opinion of you, others, here and on WOV. That is my right. I do my level best to argue the topic, and not attack the person. You've already expressed irritation with my style. Without checking, I think you said something about being bored by my questions ( I'll fix this if its a misquote). I might equally express frustration with what I perceive to be your style. I'm still stubbornly trying to stay on topic.
Now, as to Bob S. I'm personally offended by his name-calling here. I do not demand or really expect any apology.
"And this guys claims to be a businessman?" is a bit out of line. I know plenty of businessmen who don't lug their laptops. I know plenty of businessmen who have others do the Excel work. I think, OnceDear, that you're confusing the word "businessman" with "accountant."
I've said this before, but academic journals are not filled with articles and reviews signed "anonymous" or "OnceDear." If you're going to take public shots at someone, have the decency or intestinal fortitude to sign your actual name so people know where to send the fish.
Please explain how I am misinterpreting the question. The only condition in the original problem is that "at least one of the dice is a 2." You then use the example of a craps table where the first die lands on a 2, and then the other die spins. This is not every situation that is covered in the original problem. What about the example of the first die landing on 4, and the other die spins and eventually comes to rest showing a 2. This situation is also covered in the original problem.Quote:
Originally Posted by Alan Mendelson
Alan, Please do not credit me with agreeing in any way shape or form, that I agree with your 1/6 answer to the original question as asked and upon the additional common sense conditions that we agreed. vis-a-vis Assertions that the partner always called out if there was a two and that the partner saw both dice.Quote:
Originally Posted by Alan Mendelson
I have unconditionally agreed that the probability is 1/6 where you set aside one die as a two and go on to cast just a second die. I don't think anyone ever disagreed to that answer to that different question. ( Except when one member agreed breifly in error and later retracted that agreement)
And in this example the answer is still 1/6.Quote:
Originally Posted by 1in11
'And this guys claims to be a businessman'Quote:
Originally Posted by redietz
I did not add a '?' to that did I? You implied it. It was an assertion and not a question.
OK. granted I have not heard or read the actual words 'I am a businessman' from Alan. So maybe that assertion is incorrect. I apologise to Alan if Alan makes no claim to be a businessman, especially if he considers it an insult to be called a businessman.
The answer to what is 1/6?Quote:
Originally Posted by Alan Mendelson
I humbly step aside and let OnceDear (still anonymous, mind you) set the forum record for "unaware-I'm-obnoxiousness." The "aware-I'm-obnoxiousness record" is still up for grabs, but a certain reinstated member has set the bar quite high. OnceDear, you have some work to do, but I'm confident you'll at least make a run at it.
Well that settles it because that in effect was the information in the original question.Quote:
Originally Posted by OnceDear
How are these two pieces of information equivalent: At least one of the dice is a 2, and I can determine with certainty which die is a 2?Quote:
Originally Posted by Alan Mendelson
As long as one of the dice is a 2 the 1/6 answer applies. It doesn't matter which or even if both show 2. And that is the same thing you OnceDear said you would unconditionally agree to. Saying that at least one die shows a 2 and setting aside one die as a two means the same thing in the language I speak.
No it doesn't. it would only 'settle it' if IN FACT "that in effect was the information in the original question."Quote:
Originally Posted by Alan Mendelson
I and many many others assert quite strongly that
It is not true "that in effect was the information in the original question."
I've all along refused to argue the toss about anything other than the original question.
[*] I added that bit because Alan effectively paraphrased me and modified the meaning of what I said, so I modify the meaning back to mean what I said.Quote:
Originally Posted by Alan Mendelson
And that sir, is the absolute boiled down crux of where you are wrong.
Does not mean the same asQuote:
where you set aside one die as a two and go on to cast just a second die
Quote:
Two dice rolled and at least one of the dice is a 2.
I should have known better than to get involved with this, as it's clear that everyone here has decided that they are right, and that no amount of evidence to the contrary will change their position.
So, I will leave with this, and then go back to merely lurking on the forum.
The question that Alan is answering has a solution of 1/6.
The question that I am answering has a solution of 1/11.
The question as posed in post #1 is the question that I am answering.
The question as posed in post #3 is the question that Alan is answering.
I don't know any other way to express this, other than the attempts that I have previously made on this thread.
Very simply. There are only two dice. And as I said and others have said when only two dice are involved the statement "at least one of" is the same as "this die" and the answer 1/6 applies.Quote:
Originally Posted by 1in11
If you don't "get it" now you never will.
Then what is the probability of rolling ace-deuce, if at least one of the dice is a 2?
So, It might seem for the moment, that If Alan doesn't "get it now", he never will. Such is life.Quote:
Originally Posted by Alan Mendelson
I assert that Alan doesn't get it now.
1/6. Do you really need an explanation?Quote:
Originally Posted by 1in11
So, by your logic, rolling 2-2 and 1-2 have the same probability?Quote:
Originally Posted by Alan Mendelson
When one die shows a 2 then 2-2 and 2-1 have the same chance of showing which is 1/6. You don't understand that?Quote:
Originally Posted by 1in11
And before you jump all over me rolling 2-2 and 2-1 do not.
Are you able to understand the difference?
The problem with this entire "debate" is that you keep asking different questions and changing questions.
Are you able to understand the difference between 2-1 and 1-2?
Of course. And the distinction is of no consequence to the original problem. This is just another question, problem or condition. You are grasping at straws trying to avoid the correct answer to the specific question. Yes you are twisting words and twisting in the wind.Quote:
Originally Posted by 1in11
2-1 and 1-2 both satisfy the condition that one of the dice is a 2. Why then are you only considering 2-1 and not 1-2?
No more. This is a waste of time.Quote:
Originally Posted by 1in11
Altering questions and changing ground rules mid-stream is a well known trait on the wizard's forum when the know-it-all's get trapped by their own neurotic need to be perceived as right, or, as with this issue also, not to be humiliated.
As we've seen, they ran straight back to the safety of WoV where they began their sour grapes badmouthing & namecalling in an attempt to rally even more of the "anonymous brave".
I agree. I'm sorry I couldn't be of any help.Quote:
Originally Posted by Alan Mendelson
The Wizard has announced on his forum that he will happily bank these bets about two dice with at least one die showing a 2.
Total 3: Lose 1
Total 4: Pay 8
Total 5: Lose 1
Total 6: Lose 1
Total 7: Lose 1
Total 8: Lose 1
All other bets are a push. A member of the Wizard's forum who also says the answer to the question is 1/6 believes the banker of these bets will lose.
I admit I can't figure out pays/odds so I would like to offer the question here.
Does the Wizard clean up or lose?
Oh Hum.... There's a spreadsheet for that.http://oncedear.com/AlansFolly.xlsxQuote:
Originally Posted by Alan Mendelson
Glad to be of service. Goodbye.
Just to make sure, you mean you'll roll a pair of dice. Any roll that doesn't yield a two will be a push, no action. Of the rolls that yield a two, the payout will be according to the above table. Is that accurate?
Did you see that spreadsheet? Can you imagine anyone in their right mind spending all that time putting something like that together that helps evade the original question while displaying all that irrelevant theory? Evenbob would be having a field day with it! Redietz has already explained the madness as to why WoV folks do such stuff.
The weather must have been lousy in the UK again today.
Took me less than a minute to create what I assume is a very similar spreadsheet.
The problem with the spreadsheet is that it does not apply to the original problem. The language of the original question is the cause of conflicting answers.
Now consider this:
After rolling one die a 2 the odds of rolling a second die as a 2 are 1/6.
The odds of rolling two dice to show 2-2 are 1/36.
And after rolling two dice when at least one die shows a 2 the odds that the other die is a 2 are 1/6.
No one disputes the first two statements but while the third statement is effectively the same situation as the first statement there are so many who say it must have a different answer of 1/11.
So it all comes down to language because all of the math is correct.
I agree that language or logic is the problem here - I would point out that the people who argue that points one and three produce different answers are also arguing that points one and three do NOT represent "effectively the same situation" at all.
I know you haven't seen my spreadsheet, but did you happen to look at the post I made here about how I would set it up? It's clumsily written but I could find no flaws when I reread it today.
You are most welcome.Quote:
Originally Posted by Rob.Singer
I did not say I was in my right mind.
It took less time to assemble than any one of my 'wordsmith' posts.
I did it as a direct and full reply to Alan as a favour to him. I'm that kinda guy.
I figured that a yes/no answer to 'Will the wizard clean up' would not quite be enough.
Back to point 1. There is some merit to what you say. It extends to 'Why would anyone in their right mind spend all that time posting to Alan's forum and generating free content for him'. That one is rhetorical!
Synergistic -- agreed.
Arc got it right also when he commented about the language of the question.
I remember back in the late 1960s there was an issue about the wording in a national standardized test -- I believe it was the SATs and they resolved the disputes from various high schools by throwing the question out and adjusting students' scores.
Now what will be interesting is what will happen if anyone actually bets against the Wizard? The problem now is that language does not equal how dice can roll. And variance could make the Wizard win or lose. And the same variance in rolling two dice could make a 1/6er win or lose.
Early in the discussion on the Wizard's forum I said this was a trick question with the question "set up" using the coin problem being misleading. Now I am certain it was a trick question.
As I pointed out the original poster's "essay" in his spoiler made me suspect hanky panky.
There is a saying in poker that you can play the cards or play the player. If I play the player and if the 1/11-ers also play the player they'd also realize we've all been had.
I said the original poster must be having a good laugh about what he caused. It's very curious and funny how he never returned to the thread he started.
To answer his question you play the player.
I agree. The problem is logic.Quote:
Originally Posted by synergistic
The correct answer is not immediately obvious. It is just the same with the two-coin puzzle -- first you'd think 50%. Also, quite similar to the Month Hall problem or the scene in the movie 21.
Alan, you keep saying stuff like, "Enough! Just prove to me it's 1/11. No games or spreadsheets etc. Just prove it!" [Not verbatim.] And that's exactly what we're constantly doing....but, you are unable to see the truth. You can lead a horse to water but you can't make it drink.
Just try the experiment.
By the same token... or flip side of the coin... you refuse to recognize the logic that the answer is 1/6.
It was a "bad question."
You can defend 1/11 forever and I can defend 1/6 forever. And the actual bet that the Wizard says he'll bank is subject to variance.
So what if the bet that he (and I) are willing to bank are subject to variance. Every bet has variance [except for very few, like maybe betting $1 on every number straight up on roulette]. The end result, though, is we'd be having a significant advantage in such a scenario. But, I'll book that bet all day and all night (as long as the bet wouldn't be some huge part of my BR).Quote:
Originally Posted by Alan Mendelson
Alan, you're saying the original question was worded poorly. Ok -- perhaps it was (I don't think so).
But, how about this, if it was worded differently (I'm not sure how else you'd word it...been worded a million times here and on WOV).....then would you agree, the answer would be 1/11? I hope this is the case.
Rob, I'm not sure what or why you're even trying to argue. I don't think there's a legitimate gambler/AP, mathematician, statistician, etc. that takes what you say seriously at all. But, to each his own.
I think the question was intentionally worded to be deceptive. It was a trick question. How you view the event will prompt a different answer. And that's clearly what happened. If we ever hear from the original poster again he will tell us he had a good laugh.
Regarding the bet? I wouldn't bank it nor would I participate in the exercise. It's just a roll of the dice, isn't it? You can debate logic and language but you can't debate how the dice land. Either side could win... or lose when dice are rolled.
And to be honest when rolling two dice the answer is not 1/6 or 1/11 but 1/36.
Of course, either bet can win. But, I'd rather put my money down when I have a positive return.Quote:
Originally Posted by Alan Mendelson
I agree, it is 1/36 when rolling two dice. But what if we're only interested in the rolls where "at least one die is a 2"? Only counting those rolls, what do you say is the chance of rolling a 2-2? Is it 1/6, 1/11, or other?
Well we are back to square one. It depends how you look at the problem. There is the case for 1/6 when one die shows a 2 yet we all agree rolling 2-2 is a 1/36 event.Quote:
Originally Posted by RS__
What makes the bet a winner for the banker is this:
In a real casino a roll of 2-2 pays 8 to 1 which is the same as the Wizard. But in a a casino you lose the 2-2 bet only when 1-3, or any 7 rolls.
With the Wizard's bet you lose any time a number is rolled that contains a 2 on one die. That's 10 losers with the Wizard vs
7 losers with the casino.
Yesyesyes, this! With the wizard's bet, there are ten losers and one winner - only one winner out of eleven total possibilities. Follow that thought around to the paradigm shift.Quote:
Originally Posted by Alan Mendelson
And this brings us back to the WORDING of the original question. I am going to ask you to read the question for what it is. When you do the answer is 1/6.Quote:
Originally Posted by synergistic
No one should take what I will now call The Wizard's Bet.
I have to correct myself. The ways to lose a hard-4 bet in a casino are:
1-3
3-1
2-5
3-4
4-3
5-2
6-1
1-6
And that's a total of 8. And the hard 4 actually pays 7 to 1. The Wizard's Bet is much worse for the "player" with a pay of 8 with ten ways to lose. It's not clear if the Wizard pays 8 to one or 8 for one but either way it's worse than the casino bet.
Maybe Alan is just trying to increase the number of hits on this forum.
RS (that's funny): First, I don't argue with self-absorbed know-it-alls; I only talk facts. Alan's done a superb job arguing every aspect of the issue for his forum--both here and there--in spite of the mistreatment & insults WoV members have responded with about him-a WoV member BTW. You ought to ask beachbumbas, mission, wizard and face why they haven't used their "suspension powers" instead of flattering me with how "gambling AP's" don't take me seriously. The only thing that matters in gambling is winning money, and that's exactly why the collection of all that so-called intellect over there couldn't face me in person when it came to my challenge of playing my strategy in front of them to prove it.Quote:
Originally Posted by RS__
Just as you did here RS, you folks are quick to talk theory and criticize others, but when it comes time to walk the walk all you can do is resort to the anonymous chest pounding. Alan won this round big time, even to the point about how the wording of the question could have been interpreted several ways similar to the Monty Hall problem, when all you guys cared about was calling him and us stupid because we wouldn't see it "your" way. Think about that the next time you guys want to argue common sense issues outside your sacred little world of self-annointed geniuses.
You really didn't look at it then, and by the tone of once dear's response, I think he took issue with your "less than a minute" comment. Regardless, his excel effort was done with only one baseline considered, and I believe WoV members have all finally acquiesced to the fact that the question proposed was deceptive and could be interpreted several ways. The 1in11 folks preferred the more complicated route, for reasons my articles state.Quote:
Originally Posted by synergistic
Looks like they're all reading this thread from WoV now, which in turn has ramped up their being humbled. For a site that likes to pride itself on being "sensitive" to others--such as to gays, transgenders, atheists, agnostics, the poor, along with other freaks of society--it hasn't taken very much for them to denigrate & namecall this forum's members simply because we're far too common sense based to see everything exactly the way they want others to see it.
Calling that spreadsheet which only told their flawed side of the story "Alan's Folly" when theorists get frustrated, is lame, and they're even going the extra mile to pick on Dan. But hey, when you belong to a forum run by an admin. who apparently had his AP gambling/better to lose $$ on a "good bet than to win a -EV bet:)" fail him (what's new) so he had to resort to the desperate measure of begging members for money, it's no wonder all that perceived intellect they like to project is taking this so hard. Maybe when they realize that 2+2=4, even on Mars, they'll be able to handle discussions like adults--even if they don't (horror of all horrors) "prevail".
I can see one of the big issues here. Alan is trained as a journalist and writer. His job has always been to make things clear, to write and explain cleanly and with as little obfuscation as possible. I happen to also be trained as a journalist and writer. We aren't trying to look clever. Looking clever means, basically, that we've failed at our expertise.
The various WoV posters are trying to be clever. They have likely not held positions where clarity and clean writing are essential, and where purposeful confused wordsmithing (first time I've used that word myself) would get you fired. This whole enterprise, as I stated initially, is about bad writing creating confusion. If a description of events is confusing, that's on the writer, not the reader. That is a flaw of the writer, not the reader. Saying "Well, if you read it carefully enough, you can figure it out," is still a failure of the writer, not the reader.
One thing for sure, the pseudo-mensa posters are going to give "old Rob" a run for obnoxiousness ratings.
P.S. I have edited some Army event descriptions. The WoV people may have been the original authors of some of those. When people do not want you to figure out what really happened or what's really going on, this is how they write.
I especially liked how they were "forced" into putting up a video of Dan losing at live poker in 2009 just because he's an admin. here. And oh, how they must HATE the fact that wizard interviewed me, and found that the guy the pseudo-mensas (love that one red) claim not to be taken seriously by math geeks & statisticians, actually has more "math & statistics" education and related applied work experience than most of their proud array of computer nerds, actuaries, math teachers, and so on. Then for some reason they went after Scoblete even though he hasn't even chimed in. Methinks Shack and/or his foreign owners need to make refresher courses on T-O-L-E-R-A-N-C-E mandatory for all the floating egos they babysit.
Alan, OK, so we agree with the Wizard's Bet there are 10 ways to lose and 1 way to win....which is 1 in 11?
Please explain how this is any different than the original problem.
Are you really asking that?Quote:
Originally Posted by RS__
I have a question: is the Wizard offering 8 to one or 8 for one?
And since each bet is a one roll bet why isn't he offering 30 to one like the casinos?
Yes, I really asked that.Quote:
Originally Posted by Alan Mendelson
I don't know if he's offering 8 to 1 or 8 for 1. I'm sure you could ask him.
I assume he's not offering 30:1 because....well....that's not what we're talking about.
Because his bet has 1 way to win, 10 ways to lose, and 25 ways to push.Quote:
Originally Posted by Alan Mendelson
2-2 on the hop has 1 way to win and 35 ways to lose.
You can make any bet that doesn't necessarily match the question asked. In this case the bet does not match the question asked. But that is what this debate is all about, isn't it? I wonder how an English professor would interpret the question? We know how you "math guys" interpret it.
I was being sarcastic when I asked why the Wiz isn't offering 30 to 1, because the bet isn't clear to begin with since we don't know if its 8 to 1 or 8 for 1. I am surprised that the difference slipped by the math guys over on the Wizard's forum.
But if the difference between 8 to 1 and 8 for 1 can slip by the math guys, I guess the phrasing of a question might also slip by.
What is encouraging is that a few on the Wizard's site do concede that if one die were set on 2, the odds would be 1/6 on the roll of a second die. By recognizing that, they should also acknowledge that the answer of 1/6 is not wrong based on the interpretation of the question.
What is becoming clear is while I have been accused of having a closed mind, it is the guys on Wizard's site who have their minds made up and have closed it to the idea that the question itself is flawed. And that's what I pointed out earlier in recounting the story about the flawed SAT question back in the 1960s.
Alan you know what's going on with these guys. They're frustrated that you made sense in your argument and in how they've now needed to change the problem and question around in order that it more closely simulate their version. And this can be readily confirmed by how insulting these geniuses who got it wrong from the start, now are. And those bets....they keep getting more and more further from the point. Oh how I wish those guys had the courage to face me at a machine.....
Actually, the more I think about it, there are only TWO possible answers to the original question:
#1 The 1/6 answer because we know one die is already a 2.
#2 The other possible answer is 1/36 because the chance of rolling 2-2 is always 1/36
The answer of 1/11 is really a "reach." I will concede that it might be the way that mathematicians approach this type of problem, but if you were playing a game with two dice would you really consult an Excel spread sheet?
I guess in an ivory tower you would.
#3 1/11 when you eliminate the 25 other outcomes like 4-3, 3-4, etc without a 2.Quote:
Originally Posted by Alan Mendelson
Be practical for a minute and step out of your ivory tower. The question is this:
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?
Would you really answer the question with this:
Or would you say: the other die has six faces, so 1 in six is a 2. Or... would you say the chance of rolling two dice to be 2-2 is always 1/36 ??Quote:
Originally Posted by jbjb
Your not looking at one die when you peek. You look at both. This is the confusing part of the whole question and can see where it's causing fits. Not that complicated. Hell, even when I first read it over there, 1/6 was the first thing I thought too. Took me about half an hour to realize that I was wrong. Also nobody changed my mind either. Again attempt this on your own and you'll see it work out.
Or would you say how many combinations of the dice satisfy the condition "at least one of the dice is a 2", and how many combinations of the dice satisfy the condition "both of the dice are a 2"?Quote:
Originally Posted by Alan Mendelson
Alan, with your understanding of the meaning of "At least one of the dice is a 2," can you tell us how many combinations of the dice can satisfy that condition?
Or is it somewhere else in the question that the wording is unclear?
This is absolutely and totally wrong. We -- the respondents -- are not looking at anything. We are only told that "At least one of the dice is a 2."Quote:
Originally Posted by jbjb
That is the only information we have, and because we are told that, we can arrive at the answer that the remaining die is a 1/6 chance of being a 2.
Let me take these statement by statement:Quote:
Originally Posted by 1in11
Statement #1 how many combinations of the dice satisfy the condition "at least one of the dice is a 2" There are two combinations. 2-2 and 2-X with X being any of the five faces on the second die that is not a 2.
Statement #2 how many combinations of the dice satisfy the condition "both of the dice are a 2"? this is easy, there is only one combination which is 2-2
Statement #3 with your understanding of the meaning of "At least one of the dice is a 2," can you tell us how many combinations of the dice can satisfy that condition? There are two combinations. Die #1 is a 2 and die #2 is any of the six numbers on that die. Or you can reverse this so that Die #1 is any of the six numbers on that die and Die #2 is the 2.
Can you tell me out of the 36 ways to roll 2 dice, how many of those ways satisfy the condition "Die #1 is a 2 and die #2 is any of the six numbers on that die. Or you can reverse this so that Die #1 is any of the six numbers on that die and Die #2 is the 2"?Quote:
Originally Posted by Alan Mendelson
The cup and person peeking is just an illusion to throw you off. There is no need for them. Surprisingly Frank Scoblete hasn't chimed in on this. Would love to hear his expansion.
All you are trying to do is get me to refer to your 1/11 answer. And I just can't. It's because the original question gives us the value of one die and to answer that original question you figure the second die.Quote:
Originally Posted by 1in11
Look guys, if the original question were different your Excel spreadsheets and your 1/11 answer might be appropriate. But I can't and won't use Excel spreadsheets when I know at least one die is a 2 and it's a matter of six possible choices on the second die.
It is NOT an illusion. IT IS THE QUESTION. And you have to respond to the question. And that's the problem with you and the others. You are making up your own rules and your own conditions and you are not responding to the question. When you respond to the question the answer can only be 1/6. Give it a rest already.Quote:
Originally Posted by jbjb