How many of those projects did not hire anyone for a researcher role?
SELECT count ( project_id )  FROM Projects WHERE project_id NOT IN  (  SELECT project_id FROM Project_Staff WHERE role_code  =  'researcher'  ) 
projects did not hire anyone for a researcher role refers to projects where project_id does not exist in Project_Staff with role_code = 'researcher'; count of these projects refers to COUNT(project_id);