Problem C

Just Sum Dice

Ahmik created a game for his schoolâ€™s carnival where players roll two dice and find the sum of the two numbers on the top faces. If this sum is a perfect square or a prime number, they win a prize. To make it more interesting, Ahmik made the two dice using a 3D printer so that they each have the numbers \(1\), \(2\), \(3\), \(5\), \(7\), and \(9\) on their faces. One of the dice is purple and the other is green.

What is the probability that a player will win a prize after rolling the dice once?

Note:

A square of any integer is called a *perfect square*. The number \(25\) is a perfect square since it can be expressed as \(5^2\) or \(5 \times 5\).

A *prime number* is an integer greater than \(1\) that has only two positive divisors; \(1\) and itself. The number \(17\) is prime because its only positive divisors are \(1\) and \(17\).

**Theme:** Data Management