'Black Ops Arcade' Doesn't Exist on Xbox 360 – You Likely Mean Call of Duty: Black Ops
There is no game titled "Black Ops Arcade" on Xbox 360.
You almost certainly want one of these:
Call of Duty: Black Ops (2010) — Full campaign, Zombies (Kino der Toten, Five, Dead Ops Arcade mini-game), Multiplayer. Disc or Digital (delisted but redownloadable if owned).
Call of Duty: Black Ops II (2012) — Future setting, Pick 10, Zombies (TranZit, Mob of the Dead, Origins).
Dead Ops Arcade / Dead Ops Arcade 2: Twin-stick top-down Zombies mini-games inside Black Ops 1 & 2 (unlock via code or Easter egg).