  The probability for two monic polynomials of a positive degree n with
coefficients in the finite field F_q to be relatively prime turns out to be
identical with the probability for an n x n Hankel matrix over F_q to be
nonsingular. Motivated by this, we give an explicit map from pairs of coprime
polynomials to nonsingular Hankel matrices that explains this connection. A
basic tool used here is the classical notion of Bezoutian of two polynomials.
Moreover, we give simpler and direct proofs of the general formulae for the
number of m-tuples of relatively prime polynomials over F_q of given degrees
and for the number of n x n Hankel matrices over F_q of a given rank
