  Here, we present results on the intrinsic collision probabilities, $ P_I$,
and range of collision speeds, $V_I$, as a function of the heliocentric
distance, $r$, in the trans-Neptunian region. The collision speed is one of the
parameters, that serves as a proxy to a collisional outcome e.g., complete
disruption and scattering of fragments, or formation of crater, where both
processes are directly related to the impact energy. We utilize an improved and
de-biased model of the trans-Neptunian object (TNO) region from the "Outer
Solar System Origins Survey" (OSSOS). It provides a well-defined orbital
distribution model of TNOs, based on multiple opposition observations of more
than 1000 bodies. In this work we compute collisional probabilities for the
OSSOS models of the main classical, resonant, detached+outer and scattering TNO
populations. The intrinsic collision probabilities and collision speeds are
computed using the \"{O}pik's approach, as revised and modified by Wetherill
for non-circular and inclined orbits. The calculations are carried out for each
of the dynamical TNO groups, allowing for inter-population collisions as well
as collisions within each TNO population, resulting in 28 combinations in
total. Our results indicate that collisions in the trans-Neptunian region are
possible over a wide range in ($r, V_I$) phase space. Although collisions are
calculated to happen within $r\sim 20 - 200$~AU and $V_I \sim 0.1$~km/s to as
high as $V_I\sim9$~km/s, most of the collisions are likely to happen at low
relative velocities $V_I<1$~km/s and are dominated by the main classical belt.
