  We calculate the probability that random polynomial matrices over a finite
field with certain structures are right prime or left prime, respectively. In
particular, we give an asymptotic formula for the probability that finitely
many nonsingular polynomial matrices are mutually left coprime. These results
are used to estimate the number of reachable and observable linear systems as
well as the number of non-catastrophic convolutional codes. Moreover, we are
able to achieve an asymptotic formula for the probability that a parallel
connected linear system is reachable.
