Question

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?

Answer 1

`(5)/(36)`

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}`