While I agree with the majority of you post, there is no way of knowing how a carrier would survive a missile strike.
I single ballistic missile may well send a carrier to the bottom.
Only if it has a nuclear warhead.
The entire concept behind the DF-21D is a fantasy, and it will never work. In fact, many actually believe it is a smoke screen, as all the other missiles in that class are actual nuclear warhead delivery systems. So shouting to the world they were launching one that is conventional at a carrier fleet might delay a response, and even cause some to question if the "explosion" from such was of a nuclear weapon, or the carrier being hit.
But the very idea is stilly in the extreme. Remember, carriers operate well outside of RADAR range of the shore. There is no way to accurately acquire one, especially with the pinpoint accuracy needed to actually strike it. You literally are talking about trying to locate, then track a moving object from over 1,000 miles away, with no way to do that. "Over the Horizon" RADAR does exist, but it is not accurate at all, giving the user little more than "An object is out there in this direction", not what is needed to know what the objects really are, and their exact location.
And a carrier is a moving target. With the flight deck being roughly the size of 3 soccer or football fields laid end to end. 40 meters across. And the DF-21D is believed to have a CEP in the range of 50-100 meters.
In other words, even if it is performing exactly as believed in the fantasy, there is a good chance it will still miss the carrier. There is a damned good reason why no nation uses ballistic missiles (other than nukes) for trying to hit moving targets.
And also, a ballistic missile would no more sink a carrier than any other single missile. Many of the most "lethal" missiles are actually not all that big, designed to poke a hole in the waterline. Not the fantasy of a missile slamming through over 200 feet of decks and bulkheads as this one claims to be able to do.