What is the 'law of large numbers' and why is it important to insurance?

The law of large numbers is a statistical principle holding that as the number of similar, independent exposure units (such as insured lives) grows larger, the actual results will tend to come closer to the expected (predicted) results. Insurance relies on this principle: by pooling a large number of similar risks, an insurer can predict aggregate losses with reasonable accuracy and set premiums accordingly, even though it cannot predict which specific individuals will suffer a loss. This predictability is what makes the spreading of risk through insurance financially workable. Understanding the law of large numbers is a foundational insurance concept tested across lines.