The liberty count gives:
Considering that in a capturing race between one eye and none, the player with the eye gets the shared liberties, the final tally is Black 10 to White 11.
Black loses in all cases.
Moonprince: Confused newby here. Will some please set up a diagram and explain why black loses? Can't black kill the inside white and make eyes?
If , White takes the entire outside group instead of the two stones.
Gronk: While this explicit method is good to see once concretely (as shown), it is an awfully hard way to evaluate capturing races. The risk of misreading is very high. I strongly recommend RichardHunter's book CountingLibertiesAndWinningCapturingRaces for a thorough treatment of how to count liberties in cases like this (and others).