Dumb luck works for me, except it leaves one niggling little problem. There should be thousands of people still alive all over the place. Every little solidly built farmhouse, every little remote area, people should be holed up everywhere. But instead we have almost no one alive. It is poor writing.
Recall that the vast majority of season one took place in a very small geographic area that was not near farmhouses and remote areas. The lack of something having been shown so far that does not fit into the story told as yet does not automatically equal "poor writing." Obviously there are other survivors we have yet to meet. This was, after all, only a six-episode season. There's only so much that can be done in that timeframe, especially since the story that was told so far relates to a few specific people who have done very little traveling over the course of that season.