We all know Romeo, he of the "Dead" series.
An idea explored in his films (Especially Land of the Dead) is that zombies can think, learn to use tools, and the like.
For example, in Day of the Dead, the zombie Bub learns to use a gun. In Land of the Dead, the zombies have "memories" and the zombie "Big Daddy" learns to operate a gun. He leads the other zombies against the human race. At the end of the film, the zombies actually withdraw instead of attacking the remaining humans.
What do you think the chances of these events are? Could zombies actually learn to think and retain memories of their lives?
Zombies learning to use guns and thinking?
Zombies resisting the urge to kill?
Zombies planning attack strategies?
(IMO, this is unlikely. Zombies are dead. Dead things can't think.)