Consider the set of polynomials (in standard form) P: the coefficients in the polynomials are integers.

Quite like Z (integers), every distinct member of P has a unique 'prime factorization'. (Although all 1st degree or higher polynomials always have factors within C (complex polynomials), they seemingly rarely have factors within P)

Then some members of P are coprime to others.

What is the probability that n randomly chosen members of P, degree z or lower, are coprime?

This is already solved for z=0, due to Eulers solution to the Basel problem and the Zeta function. This quandary seems a lot more difficult because I don't know of a way to generate prime polynomials, etc.