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# Insurance Rates and the Law of Large Numbers: Making Sense of the Math

The law of large numbers is a statistical concept that relates to probability. It is one of the factors insurance companies use to determine their rates.

## The Law of Large Numbers Defined

There are several ways to explain the law of large numbers. Unfortunately, they are all rather convoluted and confusing. Basically, the law of large numbers means that the larger the number of units that are individually exposed to an event, the greater the likelihood that the actual results of that exposure will equal the expected results.

## In Layman's Terms

Let's try to understand the law of large numbers from a different angle, using eggs as an example. Say that for every three-dozen eggs sold by a grocer, an average of one of those eggs is cracked. Therefore, we expect that every time we buy three-dozen eggs, it is likely (though not guaranteed) we will find one cracked one. The more eggs we buy, the more likely this is. If we buy 12-dozen eggs, the likelihood that one for every three-dozen will be cracked increases. If we buy 18-dozen eggs, the likelihood that one for every three-dozen will be cracked increases even more. The more eggs we deal with, the more likely we are to find that one out of every three-dozen is cracked!

How the Law of Large Numbers Relates to Insurance

Insurance companies use the law of large numbers to lessen their own risk of loss by pooling a large enough number of people together in an insured group. The size of the pool corresponds to the predictability of the losses, just like the more eggs we deal with, the more likely we are to know how many will be cracked.

For example, an auto insurance company may record and study the number of accidents caused by a very large population of 18-year-old males. They will be able to predict how many 18-year-old males will cause an accident in a given year. They will know that in a given year there is a high probability that X number of 18-year-old males will cause an accident. Knowing this, they partially can determine how much an 18-year-old male should pay for auto insurance (excluding other factors, such as the type of vehicle, region where the driver resides, etc.) This is how the law of large numbers helps insurance providers determine their rates, and why the rates vary from one type of individual to another.