Is it really probability or its calculus?

If x and y are chosen randomly from set containing the numbers $1,2,3,4,5,6$ with replacement. The probability that $\lim_{z \to 0} ( \frac{x^z + y^z}{2} )^{\frac{2}{z}} = 6$ is equal to $\frac{p}{q}$ where p and q are relatively prime. Then find the value of $p+q$ .