  In this paper, we study the Feldman-Katok metric in random dynamical systems
and establish corresponding fiber topological entropy formula, Brin-Katok local
entropy formula and fiber Katok entropy formula by replacing Bowen metric with
Feldman-Katok metric. It turns out that the Feldman-Katok metric is also the
weakest metric that makes the entropy formulae valid on random dynamical
systems.

Dynamical Systems