Same Dice In-A-Row
Suppose there are four 6-sided dice. If each of the four dice are rolled in a totally random manner (each face is equi-probable to be rolled on each die), then what is the probability that each die will land on the same number when all dice are rolled simultaneously? (I.E 1,1,1,1 or 6,6,6,6)
Note ^ denotes
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1 solution
One might be tempted at first glance to say that (1/6)^4 is the correct probability, but this is only the probability of any one face of the 6-sided die being rolled by all dice at once. To account for all 6 sides, which are equally probable to be rolled, we simply add up (1/6)^4 six times, giving us the correct answer of 6(1/6)^4 = (1/6)^3 .