Why was the forbidden tree in the Garden to begin with?

Why didn't God warn Eve of the lie Eve was going to be told from the serpent about the tree? What would have happened if Adam refused to eat of it even after Eve insisted he do so? If they hadn't disobeyed God, would they still be alive toiling in the Garden? Would they have had childrfen at all? Would they be the only two humans in the world today? Think about it!!!!