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In almost all personal injury cases, it must be shown that the defendant was at some kind of fault (acting either intentionally or negligently) in causing an injury. However, there are some activities which are so dangerous that the defendant is liable for any injuries caused by engaging in them, not matter how careful they're being. These are known as "strict liability" cases. The idea behind strict liability is that some activities cannot be made completely safe, no matter how much care is exercised. Therefore, if someone chooses to engage in one of those activities, they should be prepared to compensate anyone who is injured because of what they're doing, regardless of how careful they were.
For example, suppose that a company is engaged in the storage of explosives. This is one "abnormally dangerous" activity that clearly gives rise to strict liability. Obviously, this company, if it wants to stay in business, will take every possible precaution to ensure that the explosives do not accidentally go off, to the point that nobody could seriously argue that they're being negligent. Chances are, these precautions will pay off, making mishaps very rare.
However, suppose that some freak accident, totally beyond the company's control, causes an explosion, and somebody is injured. Such an injury couldn't be said to be the company's fault, by just about any standard. However, under strict liability, fault is irrelevant - the company has to compensate any injured party.
There are a few common activities that give rise to strict liability, and they include: the storage or transport of explosives or toxic chemicals, the keeping of wild animals, or storage of large amounts of water (in a tank, or behind a dam, for example). In addition, domestic animals (dogs, cats, etc.) which the owner knows, or should have known, are unusually aggressive can subject the owner to strict liability if they injure someone.