Irony of the Dice Problem

[redietz]

Does anyone else find it strange that one side of the debate claims that the description of the dice throw must refer to multiple events because it is a "probability" question? And yet, the only way to arrive at the fact that the math (not general usage) definition of "probability" should be assigned is because there are presumed to be multiple throws?

Now I'm from Mayberry, but something seems not quite correct with that.

[Alan Mendelson]

In order to get 1/11 you can't use one six-sided die alone.

[OneHitWonder]

The 1/6 chance is as much about probability as the 1/11 chance. The latter is the combined probability of the former's two possible sides, whether taken separately or together, and whether over one roll or many.

As far as probability is concerned, one roll suffices quite nicely.

[arcimede$]

Does anyone else find it strange that one side of the debate claims that the description of the dice throw must refer to multiple events because it is a "probability" question? And yet, the only way to arrive at the fact that the math (not general usage) definition of "probability" should be assigned is because there are presumed to be multiple throws?

Now I'm from Mayberry, but something seems not quite correct with that.

Wrong ....math is the general usage in this context. Why do you keep trying to ignore the obvious context?

[Alan Mendelson]

Arc just stop you whining. The question is specific. It deals with one throw of the dice. And one of the dice shows a 2 and that is a fixed condition.

You and all of the other "1/11ers" need a Rube Goldberg machine to come up with the 1/11 answer when simply this was a one-die, one of 6 faces solution.

[arcimede$]

Arc just stop you whining. The question is specific. It deals with one throw of the dice. And one of the dice shows a 2 and that is a fixed condition.

You and all of the other "1/11ers" need a Rube Goldberg machine to come up with the 1/11 answer when simply this was a one-die, one of 6 faces solution.

Nope, the question asks you the "probability". The one throw is just used to described the scenario. It provides the necessary parameters for computing probabilities. Your constant denial of what is being asked is getting quite ridiculous.

I'm beginning to wonder if you even understand the meaning of the word "probability".

[OneHitWonder]

Arc just stop you whining.

After you've rolled the dice once, and looked or thought about looking, there is no longer any chance for the condition "one 2 or two 2's". Except for seeing one die showing a 2, and not seeing the other one. The specific roll - any roll, each is specific - will settle on EITHER the one 2, or the two 2's, without question of which. Quantum mechanics doesn't extend into the macro realm, in which we reside 100% of the time.

You can't roll out the chart! Especially, not before the dice. Nor stand there thinking about this before doing either to not commit yourself.
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Beyond this, intuitively, there is no rational way to equate "one 2 or two 2's (as an unknown)" and "rolls of one 2, plus rolls of two 2's (= 11)". Or's and and's aren't the same thing.

[OneHitWonder]

The study of probability helps us figure out the likelihood of something happening. For instance, when you roll a pair of dice, you might ask how likely you are to roll a seven. In math, we call the "something happening" an "event."

The probability of the occurrence of an event can be expressed as a fraction or a decimal from 0 to 1. Events that are unlikely will have a probability near 0, and events that are likely to happen have probabilities near 1.*

In any probability problem, it is very important to identify all the different outcomes that could occur. For instance, in the question about the dice, you must figure out all the different ways the dice could land, and all the different ways you could roll a seven.

* Note that when you're dealing with an infinite number of possible events, an event that could conceivably happen might have probability zero. Consider the example of picking a random number between 1 and 10 - what is the probability that you'll pick 5.0724? It's zero, but it could happen.

Likewise, when dealing with infinities, a probability of 1 doesn't guarantee the event: when choosing a random number between 1 and 10, what is the probability that you'll choose a number other than 5.0724? It's 1.

http://mathforum.org/dr.math/faq/faq.prob.intro.html

The interesting part of this *ed stuff is that probabilities often require some sort of logical intervention. There are an infinite number of real numbers between one and ten, and hence any one of those has zero chance or width in the lot (in the mathematical limit at infinity).

[Rob.Singer]

Let's try this, which is understandable. Math as a tool can be useful, but only as a tool. When used as a crutch as a way of trying to define everything that happens in everyday life, it becomes the lifeline of a fool. That is why people were given the far more complex entity attached to their necks. It allows the unique characteristic of common sense to come into play. And that will trump pure math every single time.

[OneHitWonder]

Math as a tool can be useful, but only as a tool. When used as a crutch as a way of trying to define everything that happens in everyday life, it becomes the lifeline of a fool.

Fairy tale endings happen by the book; reality, not so much. The reason that some people seem to be perpetual students. They can't help themselves. More scattered equations to learn, to plug in more numbers... to feel happy again.

Better to learn how to derive a few equations, and hence know also their limitations. What happens in general rarely happens in specific. Same for the plural in the singular.

You think that with all of the math talk over the years at the Wizard's, and all of the vain attempts at adding onto the literature of the well-known probability paradoxes of this nature, one of the "geniuses" over there might have realized this. It's possible to be too analytical.