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Two fair dice are rolled and the absolute value of the difference of the outcome is denoted by $$\displaystyle X$$. What are the possible values of $$\displaystyle X$$, and the probabilities associated with them. Finally a problem that does not lead to confusion. $$\displaystyle X = |6-0| = |0-6| = 6$$ $$\displaystyle X= |6-1| = |1-6| = 5$$ $$\displaystyle X = |6-2| = |2-6| = 4$$ $$\displaystyle X = |6-3| = |3-6| = 3$$ $$\displaystyle X = |6-4| = |4-6| = 2$$ $$\displaystyle X = |6-5| = |5-6| = 1$$ $$\displaystyle X = |6-6| = |6-6| = 0$$ Is it correct to say that the probability to get any $$\displaystyle X$$ is $$\displaystyle \frac{1}{7}?$$

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Your dice are different from any one I have ever seen since your dice have 7 sides and each contain the numbers 0,1,2,3,4,5,6. You should make a Cayley table similar to what Plato did but instead of putting (2,6) for example, I would put 4. Label the left hand side and the top 1 2 3 4 5 6 and STOP using 0 as a face on a die.
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SupremeCookie said: A lot of the outcomes are missing, what about e.g. (5,0), (5,1),...(4,0),(4,1), ect...? Click to expand... ahhh mouse slip. I did only the 6. CaptainBlack said: You can't throw a "0" on a D6. Click to expand... The zero is problematic. Plato said: Here are all thirty-six of the pairs. Now just count. $$\displaystyle \begin{array}{*{20}{c}} {(1,1)}&{(1,2)}&{(1,3)}&{(1,4)}&{(1,5)}&{(1,6)} \\ {(2,1)}&{(2,2)}&{(2,3)}&{(2,4)}&{(2,5)}&{(2,6)} \\ {(3,1)}&{(3,2)}&{(3,3)}&{(3,4)}&{(3,5)}&{(3,6)} \\ {(4,1)}&{(4,2)}&{(4,3)}&{(4,4)}&{(4,5)}&{(4,6)} \\ {(5,1)}&{(5,2)}&{(5,3)}&{(5,4)}&{(5,5)}&{(5,6)} \\ {(6,1)}&{(6,2)}&{(6,3)}&{(6,4)}&{(6,5)}&{(6,6)} \end{array}$$ Click to expand... I have already done the 6. Remove |6-0|, so we have X =,0,1,2,3,4,5. There is a clear pattern what will happen for the rest. 5 4,4 3,3,3 2,2,2,2 1,1,1,1,1 0,0,0,0,0,0
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Here are all thirty-six of the pairs. Now just count. $$\displaystyle \begin{array}{*{20}{c}} {(1,1)}&{(1,2)}&{(1,3)}&{(1,4)}&{(1,5)}&{(1,6)} \\ {(2,1)}&{(2,2)}&{(2,3)}&{(2,4)}&{(2,5)}&{(2,6)} \\ {(3,1)}&{(3,2)}&{(3,3)}&{(3,4)}&{(3,5)}&{(3,6)} \\ {(4,1)}&{(4,2)}&{(4,3)}&{(4,4)}&{(4,5)}&{(4,6)} \\ {(5,1)}&{(5,2)}&{(5,3)}&{(5,4)}&{(5,5)}&{(5,6)} \\ {(6,1)}&{(6,2)}&{(6,3)}&{(6,4)}&{(6,5)}&{(6,6)} \end{array}$$
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george357 said: Two fair dice are rolled and the absolute value of the difference of the outcome is denoted by $$\displaystyle X$$. What are the possible values of $$\displaystyle X$$, and the probabilities associated with them. Finally a problem that does not lead to confusion. $$\displaystyle X = |6-0| = |0-6| = 6$$ $$\displaystyle X= |6-1| = |1-6| = 5$$ $$\displaystyle X = |6-2| = |2-6| = 4$$ $$\displaystyle X = |6-3| = |3-6| = 3$$ $$\displaystyle X = |6-4| = |4-6| = 2$$ $$\displaystyle X = |6-5| = |5-6| = 1$$ $$\displaystyle X = |6-6| = |6-6| = 0$$ Is it correct to say that the probability to get any $$\displaystyle X$$ is $$\displaystyle \frac{1}{7}?$$ Click to expand... You can't throw a "0" on a D6.
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george357 said: Two fair dice are rolled and the absolute value of the difference of the outcome is denoted by $$\displaystyle X$$. What are the possible values of $$\displaystyle X$$, and the probabilities associated with them. Finally a problem that does not lead to confusion. $$\displaystyle X = |6-0| = |0-6| = 6$$ $$\displaystyle X= |6-1| = |1-6| = 5$$ $$\displaystyle X = |6-2| = |2-6| = 4$$ $$\displaystyle X = |6-3| = |3-6| = 3$$ $$\displaystyle X = |6-4| = |4-6| = 2$$ $$\displaystyle X = |6-5| = |5-6| = 1$$ $$\displaystyle X = |6-6| = |6-6| = 0$$ Is it correct to say that the probability to get any $$\displaystyle X$$ is $$\displaystyle \frac{1}{7}?$$ Click to expand... A lot of the outcomes are missing, what about e.g. (5,0), (5,1),...(4,0),(4,1), ect...?
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