Which leads me to believe people are really stupid, or really gullible, or both.
Neither, actually. You see, you made this peculiar statement - "They make predictions about likely things, and they happen". Now the underlying fact is that since those events are imminent they are bound to occur. The whole concept of predictions, in my opinion, seems to be relative to a person.
Let me take an example, if there is a small, cotton textile industry near a lake and two people notice it, say Person A and Person B. Person A notes that after a few months the lake will be filled with filth, while Person B makes no such assumptions. However, it so happens that what Person A had predicted turned out to be true! This is more than obvious since Person A arrived at an obscure but logical conclusion from what he noticed.
If you see a man giving out candy to children and he offers it to you as well, would you not be tempted to take it? Albeit, you will have a tad bit of hesitation but ultimately you'd give in. Humans are very biased towards the "go-with-the-flow" theory. It's the reason why people lay their trust in these self-proclaimed psychics.
