Law of Large Numbers

Example

“Thanks to the law of large numbers, the insurance company can confidently predict that approximately 2% of their 100,000 auto policyholders will file claims this year, even though they can't predict which specific drivers will have accidents.”

Memory Tip

Think 'Larger groups = Larger accuracy' - the more people in the insurance pool, the more predictable the results become.

Why It Matters

This principle makes insurance possible and affordable by allowing companies to spread risk across many policyholders and predict losses with confidence. It explains why insurance gets cheaper as more people participate and why niche or small group insurance can be expensive or unavailable.

Common Misconception

People often think this law means that if something hasn't happened recently, it's 'due' to happen soon (like assuming you're safer because your neighborhood hasn't had burglaries lately). The law actually shows that each individual event's probability remains the same regardless of recent outcomes.

In Practice

An insurance company insuring 10,000 homes might predict 50 fire claims annually based on a 0.5% probability. In year one, they might see 43 claims, year two might have 58 claims, but over 10 years, the average will very likely be close to 50 claims per year. This predictability allows them to set premiums at $500 per home annually, collecting $5 million to pay approximately $2.5 million in claims while covering expenses and profit.

Etymology

Mathematical concept formalized by Swiss mathematician Jakob Bernoulli in the early 18th century, later adapted to insurance and actuarial science in the 19th century.

Common Misspellings

Related Terms

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