Why do people experience fear?

Why do people experience fear?

There's the obvious stuff like you're in the wild and a lion is running at you.

But there are also situations in civilized society where people experience fear but there's no immediate physical danger like the lion in the wild situation. Often times people fear that they will have an emotion in the future. Consider what people mean by "stage fright". Somebody is having an emotion about something that hasn't happened yet. They imagine the future where they do something on the stage that the audience will respond negatively to, like laughing at the person on stage or shaming him or whatever. So the person on stage recognizes that they might feel bad if they get laughed at or shamed and they are having an emotion (fear) about that potential future emotion.

One way to think of fear is this: You have a problem and you don't believe that you'll solve it. 

Often times people feel fear when they encounter a problem while having done no problem-solving work on it, problem-solving work that they already know how to do. They don't try to recall previous solutions to similar problems that could potentially work for this problem. They don't try to brainstorm and criticize their way to a solution. They don't try to enlist other interested parties to help solve their problem. They don't keep a journal about their thoughts/emotions.

This is weird because people routinely do this stuff already for some problems but not others. For example, parents of babies do a basic thing where they try everything they know of until the baby responds well. They check everything: hungry? thirsty? sleepy? full diaper? etc etc until the baby is happy. Dog owners do the same thing.