## Six-sided Die

A 6-sided die is labeled with the first prime numbers instead of the first integers $1$ to $6$. The die is rolled twice. What is the probability that the sum of the rolls is a prime number?
Source: NCTM Mathematics Teacher 2008

SOLUTION
Table method

The table shows there are $6$ outcomes in which the sum of the rolls is a prime number.
Probability = $6/36=1/6$.

Alternative method
Number of possible outcomes
$6\times 6=36$
Number of desirable outcomes
We need only look at the sum of $2+x$ because we want an odd sum
$2+3=5$
$2+5=7$
$2+7=9$
$2+11=13$
$2+13=15$
Of these sums only $5,7$, and $13$ are prime number. We double the count to $6$ because we could toss $2$ and $3$ or $3$ and $2$.
Probability = $6/36=1/6$.

Answer: $1/6$