  Random metastability occurs when an externally forced or noisy system
possesses more than one state of apparent equilibrium. This work investigates a
class of random dynamical systems, arising from perturbing a one-dimensional
piecewise smooth expanding map of the interval with two invariant subintervals,
each supporting a unique ergodic absolutely continuous invariant measure. Upon
perturbation, this invariance is destroyed, allowing trajectories to randomly
switch between subintervals. We show that the invariant density of the randomly
perturbed system may be approximated by an explicit convex combination of the
two initially invariant densities, obtained by averaging. Further, we also
identify the limit of the second Oseledets space, or coherent structure, as the
perturbation shrinks to zero. Our results are applied to random paired tent
maps over ergodic, measure-preserving, and invertible driving systems. Finally,
we provide generalisations to systems admitting more than two initially
invariant sets.
