  We prove non-uniqueness in law of the three-dimensional magnetohydrodynamics
system that is forced by random noise of an additive and a linear
multiplicative type and has viscous and magnetic diffusion, both of which are
weaker than a full Laplacian. We apply convex integration to both equations of
velocity and magnetic fields in order to obtain the non-uniqueness in law in
the class of probabilistically strong solutions.
