Exact and approximate quantum mechanical calculations of reaction probabilities and cumulative reaction probabilities have been carried out for the F+H-2 reaction on the ab initio adiabatic potential energy surfaces by Stark and Werner (SW) and by Hartke, Stark, and Werner (HSW), the latter including spin-orbit corrections in the entrance channel. These data have been employed to obtain thermal rate constants for the title reaction in the temperature range 200-700 K. The exact and approximate results have been compared with experimental determinations and previous theoretical predictions. In particular, the reaction probabilities obtained on the HSW surface are found to be in very good agreement with recent calculations by Alexander [J. Chem. Phys. 109, 5710 (1998)] based on the exact treatment of spin-orbit and Coriolis coupling for this system. However, the rate constants calculated on the HSW PES are systematically lower than the experimental values, which indicates that the height of the adiabatic potential energy surface is too high. Furthermore, an estimate of cross sections from the reaction probabilities calculated by Alexander shows that the contribution to the low temperature rate constants from spin-orbit excited F(P-2(1/2)) atoms through nonadiabatic channels is very small and, thus, nonadiabatic effects are not sufficient to bring the calculated rate constants to a better agreement with the experimental measurements.