We tend not to realize the amount of data our unconscious minds process, informing our conscious decisions, without any effort at all.
Exactly. Lots of the time when people talk about things like "a gut feeling" or "common sense" or "it just makes sense" or "it doesn't seem likely" or any of the dozen other phrases we toss around, it is that unconscious process back there doing the stats and sending us a message. Like Glenn said, "When someone says they don't take into account the odds, that's just not true. We predict possible outcomes on most things we do." We just don't realize that we are making those predictions based on what we think the odds are.