I would say the chances of encountering a bear or mountain lion are slim to none. I do a lot of hiking (as I live in Colorado) during the summer, and have yet to see either a bear or a mountain lion. I just got back from a trip to the San Juans, and other that a few mulies and a bunch of mountain goats, I didn't see much else. That's not to say it's not possible, and I guess it's always better to be safe than sorry.