## Challenge 362: A likely solution

The values *p* and *q* in the quadratic expression 2x^{2} - *p*x +*q* are determined by throwing two standard fair cubical dice, one red and one blue.

*p* is given by the value shown by the red die and *q* is given by the value shown on the blue die.

What is the probability that the equation 2x^{2} - *p*x + *q* = 0 will have a solution that is a prime number?

Make your solution as efficient as you can!