No you do not...How juvenile.
Then by all means, explain how could a warhead with a CEP of 300-400 meters...
DF-21 - China Nuclear Forces
Can hit a maneuvering target whose length is equal to or less than the CEP figure itself.
Circular Error Probable (CEP)
A measure of missile accuracy. A missile's CEP is the radius of a circle around the target in which 50% of the warheads aimed at that target will land.
CEP 400m means there will be 50% probability that the warhead will land within the circle of 400m radius. This circle will have an area of 400*400*pi=502,654m^2
By ignoring system error (as system error is a constant deviation and can be adjusted in many cases), a carrier will be in the center of the circle.
Suppose the carrier is Nimitz class, to simplify, it has an area of 300*100=30,000m^2.
To underestimate the hit probability, suppose within the circle, the missiles will be evenly distributed in probability while landing on the target area.
30,000/502,654 = 0.06. This means every 40 missiles launched, there will be 20 in the circle, and roughly 1 (0.06*20) will hit the carrier.
Let’s further assume that the fatal area of the carrier is not 30,000m^2, rather it is 100*50=5,000m^2. Thus, 5,000/502,654 =0.01. This means every 200 missiles launched, there will be 100 in the circle, and 1 will hit the vital spot.
A typical cost of Nimitz class carrier is 4.5billion. A Df-21 is about $0.82mil each.
Catalog For simplicity, let it be 1mil each as China is becoming more costly. If PLA launch $1billion worthy of missiles (1000), 500 will be within the circle, 5 will hit the vital spot. That pretty sure is enough to make warlords cry. Economically, 1:4.5 is not a bad business, though it’s pathetic compared with our Wall Street alligators’ maneuver, but political and military impact will be far more profound than what those alligators and warlords combined can do. So actual value (to PRC) is far beyond. Thus I don’t doubt PRC may have prepared 5000 or more for carriers.
A more accurate estimation is that, the distribution of probability is normally of Gaussian type (or often called bell shaped if you attended US high school). Thus, it is more concentrating towards the center, not evenly probable withing the area. With a simple linear interpolation, the hit-target probability will be nearly doubled. So, that compansates for (if) 30% of the missiles that will eventually be shot down (it’s hard if allegedly 10 Mach is true, and I assume it may come down on to a carrier vertically or near vertically), 1000 launches can still manage to have 5 hits on the vital spot.
True that actual estimation is very complex. For instance, if the carrier is maneuvering at 15m/s (a typical Nimitz top speed), the target-seeking mechanism, the operational environment, the operators’ quality, etc. are all vital in contributing to success/failure. Frankly, many of these are top secrets on both sides. But to say no hit at all is a joke: simple high-school statistics: with increased number of experiments, the chance increases linearly. Theoretically, the probability to hit a lottery is like one that a huge meteor destroys the earth, yet people get it and the earth is still alive.
Hope it helps a little bit.