In a cubic dice, the sum of the numbers on 2 opposite faces is 7, why are numbers arranged in such a way? Would the result of throwing a dice (1 or more times) still yield a random number if the numbers were arranged differently? Thanks.
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A fair die is equivalent to a random integer generator on the set $\{1, 2, 3, 4, 5, 6\}$. Of course, the order of the integers doesn't matter, so neither do the arrangement of the numbers on the die.
But to answer your question about why this arrangement, according to http://en.wikipedia.org/wiki/Dice, this is presumably so the 1, 2, and 3 faces of the die share a vertex, which is aesthetically pleasing.
answered May 4, 2013 at 14:08
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1$\begingroup$ It is just standardized in a fixed way: faces $1,2,3$ follow the right-hand-rule and $4,5,6$ are placed so that they follow the sum rule. $\endgroup$– BerciMay 4, 2013 at 14:19
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$\begingroup$ Thanks for the answer. I some how feel that the sum of numbers resulting from independent throws of the dice (or the throw of 2 such dice and summing the value on their face) is biased because the arrangement of numbers follow a pattern and are not random. However, it looks like this is not true. $\endgroup$– NoChanceMay 4, 2013 at 17:42