Have I made a mistake?

[VivaLaViking]

Assume the flop leaves you with 10 outs.

Your probability of improving your hand by the river is:
[1 - (37/47)(36/46)] * 100 ~= 38.4%
Your probability of improving your hand immediately on the turn is:
(10 * 100) / 47 ~= 21.28%
After not improving on the turn your probability of improving in the river is:
(10 * 100) / 46 ~= 21.74%

Why does this math indicate that the probabilty increased for the river draw over the turn draw?