Ball Hitch Lawn Tractor

I have a small murray lawn tractor 14.5hp, it has a plate with a hole in the back bumper area for a hitch ball - but when I tried to put some of my 1 7/8" balls on it, the threaded shaft is too large to fit in the hole on the mower plate (its close but just won't go) - whats up with that? do they sell a seperate hitch ball that you have to buy someplace thats Just for these lawn tractors? what a scam if so. Where can I get a 1 7/8" hitch ball that will actually fit in the hole on the back of the lawn tractor? Thanks for any help. This doesn't make alot of sense to me why they wouldn't make it the standard hole size opening that all hitch balls use.
Thanks for the replies - yes its an older (2000) tractor, so I guess it pre-dates the 3/4" opening. I think the hole is 1/2" or 5/8". I was only going to move around a small empty trailer, very light, so hopefully that would not be a problem.