An inductive inference to X is said to be cogent so long as the data are best explained by positing X. We do this all time. For example, given our experience of human beings, we conclude that if Socrates is a human being, then Socrates is mortal. After all, every other human we observe is mortal, and there doesn't appear to be anything about Socrates that would make him an exception.
The Bible exposes a number of false inductive inferences. For example, in 2 Chronicles 32:13-14, King Sennacherib of Assyria has this to say to Judah: "Do you not know what my fathers and I have done to all the peoples of other lands? Were the gods of the nations in those lands able to save their land from my hand? Who among all the gods of those nations which my fathers put under the ban was able to save his people from my hand? Will your god, then, be able to save you from my hand?"
Sennacherib's point is simple enough: the god of every other nation X was unable to save X. Yahweh is the god of Israel. Therefore, Yahweh will most likely fail to save Israel.
Of course, we later read that Sennacherib's invasion fails (2 Chronicles 32:21-23). Why is this?
Inductive inferences are only cogent insofar as there is uniformity in certain key analogies. However, there is a disparity between the gods of the nations that Sennacherib conquered and the God of Israel, Yahweh - namely, Yahweh is maximally great. A cogent inductive argument would have taken the finitude of these other gods into account.