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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