In a real galaxy, the two black holes would eventually coalesce due to emission of gravitational waves. The spin axis of the coalesced hole will be aligned with the angular momentum axis of the orbit of the pre-existing binary. Hence, a mechanism like rotational Brownian motion that affects the orbits of binary black holes can also affect the distribution of black hole spins. This may explain in part why the spin axes of supermassive black holes appear to be randomly aligned with respect to their host galaxies.