If two fair dice (with faces numbered 1,2,3,4,5,6) are tossed together, what is the probability that the total score will be a perfect cube?

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If two fair dice (with faces numbered 1,2,3,4,5,6) are tossed together, what is the probability that the total score will be a perfect cube?

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Thanh Hà 3 years 2021-09-03T05:49:33+00:00 1 Answers 36 views 0

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  1. Nem
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    2021-09-03T05:50:43+00:00
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    Answer:

    \frac{5}{36}

    Step-by-step explanation:

    There are 6^2=36 non-distinct sums that can be achieved when rolling two fair sided dice.

    The smallest of these sums is 1+1=2 and the largest of these sums is 6+6=12. Within this range, there exists only one perfect cube, 2^3=8.

    Count how many ways we can achieve a sum of 8 with two dice:

    \begin{cases}2+6=8,\\6+2=8,\\3+5=8, \\5+3=8,\\4+4=8\end{cases}\\\\\implies \text{5 ways}

    Thus the probability the total score (sum) will be a perfect cube when rolling two fair six-sided dice is equal to \boxed{5/36}

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