Going by your formula....
300,000 Ohio archers divided by 90 entries= .0003
Since we're checking math and all.....those 90 entries were only for one quarter as well.
If we extrapolate (seems to be the thing to do around here, lately...lol)....you stand an 80% better chance of bagging one in OH than you do in NC.
That's .0012 v. .0004 (suited to match our state's # of bowhunters).
You have 3X the bowhunters we do.....and 9X the number of entries. Competition and pressure doesn't seem to be as much of a detriment as some would have us think! Having an abundance of available targets seems to trump those factors...and in a BIG way.
But like I said.....You're sayin' there's a chance!