Are Different Dice Color Outcomes Considered the Same?

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The discussion revolves around whether outcomes from rolling colored dice are considered the same or different. One participant suggests that outcomes yielding the same total, like {3[red] 4[blue]} and {4[red] 3[blue]}, should be regarded as identical. However, others argue that the distinct colors of the dice imply that the outcomes are different, emphasizing that the individual values matter in probability scenarios. The analogy of flipping coins illustrates that order matters, reinforcing the idea that different arrangements of the same numbers are unique outcomes. Ultimately, the consensus leans towards treating the outcomes as different due to the significance of color and order in the results.
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erm... I am facing one question that confused me..
the problem as abt the problem on problem..
the question is like this: there is two one red six-sided dice, one blue six-sided dice, and one red six sided dice.
One possible outcome is (1, 2), i.e. the red dice shows “1”, and the blue dice shows “2”. and the question ask: are {3[red color] 4 [blue color] } and {4[red] 3[blue]} considered the same outcome or different??

my idea is that should be same, as the total result is 7 for both..
wanna ask opinion from u guys..

thanks
 
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kecontroversy said:
erm... I am facing one question that confused me..
the problem as abt the problem on problem..
the question is like this: there is two one red six-sided dice, one blue six-sided dice, and one red six sided dice.
One possible outcome is (1, 2), i.e. the red dice shows “1”, and the blue dice shows “2”. and the question ask: are {3[red color] 4 [blue color] } and {4[red] 3[blue]} considered the same outcome or different??

my idea is that should be same, as the total result is 7 for both..
wanna ask opinion from u guys..

thanks
They are probably considered different since you went to the trouble of having two color. It depends what you are doing, sometimes people who are only concerned about the sum use two colors, usually in probability problems nonidentical dice implies that we care what their individual values are.
 
kecontroversy said:
erm... I am facing one question that confused me..
the problem as abt the problem on problem..
the question is like this: there is two one red six-sided dice, one blue six-sided dice, and one red six sided dice.
One possible outcome is (1, 2), i.e. the red dice shows “1”, and the blue dice shows “2”. and the question ask: are {3[red color] 4 [blue color] } and {4[red] 3[blue]} considered the same outcome or different??

my idea is that should be same, as the total result is 7 for both..
wanna ask opinion from u guys..

thanks

They should be different since they are different outcomes of the experiment. It helps to think of things in terms of how the experiment can turn out. For example say you flip two fair coins, what is the sample space?

(H,H), (H,T), (T,H), (T,T)

Notice that (H,T) is not the same result as (T,H)

Hope that helps
 
I was reading a Bachelor thesis on Peano Arithmetic (PA). PA has the following axioms (not including the induction schema): $$\begin{align} & (A1) ~~~~ \forall x \neg (x + 1 = 0) \nonumber \\ & (A2) ~~~~ \forall xy (x + 1 =y + 1 \to x = y) \nonumber \\ & (A3) ~~~~ \forall x (x + 0 = x) \nonumber \\ & (A4) ~~~~ \forall xy (x + (y +1) = (x + y ) + 1) \nonumber \\ & (A5) ~~~~ \forall x (x \cdot 0 = 0) \nonumber \\ & (A6) ~~~~ \forall xy (x \cdot (y + 1) = (x \cdot y) + x) \nonumber...
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