This is to do with the relative stabilities of the free radicals produced. Here is a schematic diagram showing the two possibilities for propene (similar mechanism, also with two free radical possibilities like propane):
As you can see, a more stable and less stable free radical is produced. The stability depends on how many carbons are attached to the carbon with the unpaired electron. In the diagram, the free radical where two carbons are attached is more stable than the free radical with one carbon attached.
As a general rule, the stability will be greatest in tertiary free radicals, then in secondary, and least stability in primary.
This is due to the inductive effect of carbons bonded to the carbon with the unpaired electron:
Carbons bonded to the free radical carbon are able to 'move' some of their electron density over to the free radical carbon, stabilising it. This is due to something called sigma conjugation, which we needn't go into.
But in summary, both free radicals are formed, as seen in the first diagram. Both free radicals go onto generate products, but much more come from the more stable species. Therefore, in fact both carbons possible in propane end up with the unpaired electron, but the route involving the secondary free radical species is more successful and gives the major product. The route involving the primary intermediate gives a minor product.