A few years ago the figure was "several hundred" but the exact number is fluid because some people (like Matthew) are paid to work on Fedora full time, while others work on Fedora as part of their job but not their whole job.
It's also further confused by the fact that some Red Hatters contribute to Fedora but not as part of their day job.
I think it'd be fair to say more than 60% of the work that goes into Fedora's official releases is paid for by Red Hat. Maybe more. If you factor in spins and such, it might be less than 60%.
Thanks for the correction on the title.