You could also probably just create the one sphere, delete the faces for the hold, select the border edges and extrude inwards (locally). Then, just simply add a couple loops to sharpen the edges like effacer mentioned. Of course this only makes sense if you don't need a complete solid object inside the outer sphere. Maya really needs the equiv. of Max' shell modifier or Silo's "Shell" to quickly "thicken" objects.
"Terminat Bora Diem, Terminal Auctor opus."