> a majority of football and men's basketball programs are profitable

A majority of Division I programs. Only 252 out of 674 football programs and 351 out of 1099 men's basketball programs are Division I.

Division II[1] football and men's basketball programs are universally money losers. Every single one lost money. The Division III report[2] doesn't include as much detail, but I doubt that any of them are profitable either.

[1] http://www.ncaa.org/sites/default/files/2015%20Division%20II...

[2] http://www.ncaa.org/sites/default/files/2015%20Division%20II...