Is it really probability or its calculus?

Calculus Level pending

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 $$p+q$$.

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