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

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 $\boxed{5/36}$