  We compute the probability distribution of the invariant separation between
nucleation centers of colliding true vacuum bubbles arising from the decay of a
false de Sitter space vacuum. We find that even in the limit of a very small
nucleation rate per unit Hubble volume the production of widely separated
bubble pairs is suppressed. This distribution is of particular relevance for
the recently proposed ``colliding bubble braneworld'' scenario, in which the
value of Omega_k (the contribution of negative spatial curvature to the
cosmological density parameter) is determined by the invariant separation of
the colliding bubble pair. We also consider the probability of a collision with
a `third' bubble.
