Well, the tickets where y'all fill in the bubbles with pencil to choose numbers and the form can be read by an optical scanner are surely not randomly generated

Well, the tickets where y'all fill in the bubbles with pencil to choose numbers and the form can be read by an optical scanner are surely not randomly generated. People will draw pictures, play birthdays, and attempt to choose layouts that "look random", none of which result in a uniform ticket distribution, which is what most people seem to mean when they say that something is "random". The takeaway is that "distributed uniformly at random" is not a great assumption at all when inputs are generated by a process. It's one of the relatively few things I did learn in my graduate algorithms class.