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It kind of depends on what's wrong with the screen. If it looks like it's been hit or cracked, they'll call it accidental and it won't be covered. That's true for Applecare too.

It the screen is plain old dead, or has some kind of weird pattern showing that appears to be a build problem, that would be covered under the regular warranty or Applecare.

(In other words, Applecare doesn't really give you any protection over what the regular warranty would, it's just more time)
 
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