  We solve the Anderson localization problem on a two-leg ladder by the
Fokker-Planck equation approach. The solution is exact in the weak disorder
limit at a fixed inter-chain coupling. The study is motivated by progress in
investigating the hybrid particles such as cavity polaritons. This application
corresponds to parametrically different intra-chain hopping integrals (a "fast"
chain coupled to a "slow" chain). We show that the canonical
Dorokhov-Mello-Pereyra-Kumar (DMPK) equation is insufficient for this problem.
Indeed, the angular variables describing the eigenvectors of the transmission
matrix enter into an extended DMPK equation in a non-trivial way, being
entangled with the two transmission eigenvalues. This extended DMPK equation is
solved analytically and the two Lyapunov exponents are obtained as functions of
the parameters of the disordered ladder. The main result of the paper is that
near the resonance energy, where the dispersion curves of the two decoupled and
disorder-free chains intersect, the localization properties of the ladder are
dominated by those of the slow chain. Away from the resonance they are
dominated by the fast chain: a local excitation on the slow chain may travel a
distance of the order of the localization length of the fast chain.
