  In this paper, we introduce the notion of distributional chaos and the
measure of chaos for random dynamical systems generated by two interval maps.
We give some sufficient conditions for a zero measure of chaos and examples of
chaotic systems. We demonstrate that the chaoticity of the functions that
generate a system does not, in general, affect the chaoticity of the system,
i.e., a chaotic system can arise from two nonchaotic functions and vice versa.
Finally, we show that distributional chaos for random dynamical system is, in
some sense, unstable.
