Dynamical models of the asteroid delivery from the main belt suggest that the current impact flux of diameter D > 10 km asteroids on the Earth is \simeq 0.5 -1 Gyr ^ { -1 } .
Studies of the Near-Earth Asteroid ( NEA ) population find a much higher flux , with \simeq 7 D > 10 -km asteroid impacts per Gyr .
Here we show that this problem is rooted in the application of impact probability of small NEAs ( \simeq 1.5 Gyr ^ { -1 } per object ) , whose population is well characterized , to large NEAs .
In reality , large NEAs evolve from the main belt by different escape routes , have a different orbital distribution , and lower impact probabilities ( 0.8 \pm 0.3 Gyr ^ { -1 } per object ) than small NEAs .
In addition , we find that the current population of two D > 10 km NEAs ( Ganymed and Eros ) is a slight fluctuation over the long term average of 1.1 \pm 0.5 D > 10 km NEAs in a steady state .
These results have important implications for our understanding of the occurrence of the K/T-scale impacts on the terrestrial worlds .