Could I fight a bear and win?

Very, very slim chance

Your only chance is if you somehow manage to jump onto his back and gouge out his eyes. Even then, you'd better hope he's not very hungry because ...

Pros: Increased sense of self-respect, the love and admiration of others. Cons: There is no follow-up / second act that can compete ...
No

There is no possibility that you could fight a bear in hand-to-hand combat and win. Furthermore, the fact that you even considered it proves that your brain is not functioning ...

Pros: Bears need food, too. Humans are still protein! Cons: No more life.