I agree with Billy Chan. This strategy isn't going to produce any results for you. It will end up being a waste of time.
You state that your goal is to generate traffic to your site. But this isn't going to do it. If you get any people to follow you based on this, they won't be the least bit interested in engaging with you. They will just be interested in the money, so it's not going to generate any traffic to your site.
Additionally, a chance to be randomly selected to win $1 to $5 is about as weak an incentive as I can think of. A guaranteed $1 to $5 prize is already a super weak prize, but now you're reducing that even more by not even guaranteeing that miniscule amount. I seriously doubt you'll get anyone to bite with such a weak offer.
Plus consider that it's not just the prize money that it's going to cost you. The overhead associated with setting up and managing the contest will cost you more than the prize itself.