I work at a company that does not do random drug testing. I got tested when I was hired, but not in the 18 years since.
However, I heard our vice president yesterday say that if marijuana is ever legalized in our state, he will see to it that random drug testing is instated at our company, and that everyone will get randomly tested at least once per year, and maybe every 6 months. Under a "one strike and you're out" policy.
I'm not sure he could legally do that, but maybe he could. I don't know. We're salaried employees, not under a union.
I've read that some states where marijuana is legal still allow employers to fire any employee who uses marijuana, even if they have a legal prescription for it.