Estimating Responses to the Dice Question

[Alan Mendelson]

If you ask; “two dice are rolled until at least one shows a deuce, what is the probability that both show a deuce?”…then there are no mistakes, it is 1/11.

That's fine until you have to make a video showing it: one die with a 2 and the 11 faces you are presenting in your answer.

[Alan Mendelson]

LOL. I understand the question perfectly. That is why I proposed a test and you refuse to run a test and see what happens. I am 100% confident of the result. You obviously are not.

You do mine first: have two dice, with one showing a 2, and show me the 11 faces in your answer.

[RS__]

That's fine until you have to make a video showing it: one die with a 2 and the 11 faces you are presenting in your answer.

That's like trying to show a coin has 2 faces using a potato....

[Alan Mendelson]

That's like trying to show a coin has 2 faces using a potato....

Exactly. You cannot show 11 faces with a total of two dice when one die is frozen showing a 2. This is why the answer of 1/11 does not answer this question.

In order to facilitate your answer of 1/11 you must use both dice -- and the question has already given you the condition that one die is a 2.

As soon as one die is identified as a 2 -- there are only six faces on the second die to be considered.

It is every bit the same as the "spinner" problem on a craps table with the first die coming to rest as a 2.

[redietz]

I'll go on record as guessing that somewhere around 82-88% of the US general population would say 1/6 as the answer.

Here's a tell. When confronted with the statistics from Alan's Facebook page regarding this question, the 1/11ers responded with comments regarding how poorly the general population does with basic math and statistics. Nobody made the comment that the author of the question must be an example of how badly math guys write because he/she led people to a "wrong" conclusion. The 1/11ers who responded criticized the readers as a group and judged them, which seems harsh considering how many readers there were. They did not criticize the author, even though the likelihood of there being one really bad author seems (if probability principles are used here) more likely than a couple hundred really bad readers.

Maybe the proper conclusion isn't "general population bad in math," but "math guys really bad at writing and evaluating others' writing."

[Rob.Singer]

Redietz, after a while you might convince RS__ that he doesn't do so well in the reading comprehension arena. One look at how he sometimes gets laughed at on WoV for his head-scratching comments probably tells that tale. But if you think you're ever gonna get arci to confess to anything other than having mensa-level reading skills, don't stay on the toilet waiting. A more apropos comment for him might be "imagine living with that". Oh....that's a moot point.

[RS__]

Redietz, after a while you might convince RS__ that he doesn't do so well in the reading comprehension arena. One look at how he sometimes gets laughed at on WoV for his head-scratching comments probably tells that tale.

Like which ones?


It's not the readers who have poor reading comprehension....I think most people don't use the proper logic when trying to determine the answer. ie: Month Hall problem.

[arcimede$]

You do mine first: have two dice, with one showing a 2, and show me the 11 faces in your answer.

Sorry Alan, but that has nothing to do with the original question. The original question is about probability. The only way to test the probability is through multiple events. The correct answer should converge rather quickly given the low number of possible combinations. Why are you unwilling to run the test which should take no more than 10-15 minutes (a half hour if you are methodical).

[arcimede$]

Exactly. You cannot show 11 faces with a total of two dice when one die is frozen showing a 2. This is why the answer of 1/11 does not answer this question.

In order to facilitate your answer of 1/11 you must use both dice -- and the question has already given you the condition that one die is a 2.

As soon as one die is identified as a 2 -- there are only six faces on the second die to be considered.

It is every bit the same as the "spinner" problem on a craps table with the first die coming to rest as a 2.

One problem Alan, that is not the question that was asked. The only way you'll be convinced is to run the test and see what answer you get. Hey, do it yourself at your own desk. All you need is a pair of dice and a piece of paper. The fact you won't do the test tells me you know you are wrong.

[Zedd]

Maybe the proper conclusion isn't "general population bad in math," but "math guys really bad at writing and evaluating others' writing."

Do you know if a ’math guy’ wrote this question? What if an English author wrote it? Anybody can write it. Then you’re back to “general population bad in math”.

[redietz]

You're absolutely correct, Zedd. That's why I put "at evaluating others' writing" at the end. If an English guy wrote it (odds against, I'd say, given the placement in a math forum and all, but point taken), that still doesn't excuse the evaluations -- or rather, lack of evaluations -- from the math-oriented folks.

I went through the same thought process when writing it, so all I can say to you is that I appreciate you reading carefully and asking the absolutely correct questions. I've learned quite a bit from this exercise, and hopefully the WoVers have, too. I have doubts about the latter.

P.S. I realize now that "or" rather than "and" should have been in that final sentence, but I'm trying to avoid "or" at this point, mainly because I'm still recovering from trying to figure out inclusive "or" versus non-inclusive. I hereby reinstate my use of "or" in normal conversation.

[OneHitWonder]

I have doubts about the latter.

I'll make it easy for you. They exist only to feed the online casinos.

The administrators are the ones who have the time to waste for the online casinos' sponsorship. We aren't getting paid to do this, let alone to try to straighten people who don't want that to begin with.

They are fairly honest over there about nobody of note really doing the AP thing, or about very few trying it for any stretch of time. But like every other gambling forum, the topics mask the gambling addictions of many.

I would bet my last dollar that 99% of them continue to lose their last dollar gambling. Just the way it is. Those people simply do not want to learn. The reason that not a single one of them has achieved anything of not. Least of all the Wizard. Talk about persons who say idiotic mundane things.

The reason that we have to discuss this over here.

[Alan Mendelson]

Sorry Alan, but that has nothing to do with the original question. The original question is about probability. The only way to test the probability is through multiple events. The correct answer should converge rather quickly given the low number of possible combinations. Why are you unwilling to run the test which should take no more than 10-15 minutes (a half hour if you are methodical).

Arc, I did use two dice and rolled them according to the original question. And each time at least one die was a 2 the other die had a 1/6 chance of also showing a 2. And with at least one die showing a 2 I was unable to find 11 faces to consider for your 1/11 answer.

Really it amazes me how I couldn't find 11 faces. Why?

[arcimede$]

Arc, I did use two dice and rolled them according to the original question. And each time at least one die was a 2 the other die had a 1/6 chance of also showing a 2. And with at least one die showing a 2 I was unable to find 11 faces to consider for your 1/11 answer.

Really it amazes me how I couldn't find 11 faces. Why?

That's not the original question. There is no mention of "the other die" in the original question. It is getting more than obvious that you know you are wrong. Otherwise, you would do the simple test. Thanks for making it so obvious.

[Alan Mendelson]

That's not the original question. There is no mention of "the other die" in the original question. It is getting more than obvious that you know you are wrong. Otherwise, you would do the simple test. Thanks for making it so obvious.

You're right Arc. There's no "other die." There are just two of them. And at least one is showing a 2.

[arcimede$]

You're right Arc. There's no "other die." There are just two of them. And at least one is showing a 2.

Exactly, there are only two conditions to the problem. That's why I proposed the test to match those conditions. You mark one row when you see "at least one 2" and you mark another row when you see "a pair of 2s". You've then met the conditions of the problem. When you are done you divide the second number into the first number and if you are right that should be very close to 6. No more than a half hour of your time (much less probably) and you've proven to yourself that you are right (or wrong).