  The problem of making predictions in eternally inflating universe that
thermalizes by bubble nucleation is considered. A recently introduced
regularization procedure is applied to find the probability distribution for
the ensemble of thermalized bubbles. The resulting probabilities are shown to
be independent of the choice of the time parametrization. This formalism is
applied to models of open ``hybrid'' inflation with $\Omega <1$. Depending on
the parameters of the model, the probability distribution for $\Omega $ is
found to have a peak either very close to $\Omega =1$, or at an intermediate
value of $\Omega $ in the range $0.03\lesssim \Omega <1$.
