Final answer:
The law of large numbers enables insurers to predict losses accurately by ensuring that the relative frequency of an event approaches its theoretical probability as more data is collected, facilitating fair premium setting for different risk groups.
Step-by-step explanation:
The law of large numbers is instrumental for insurers to make accurate predictions about losses. This law states that as the number of trials in a probability experiment increases, the experimental probability (or relative frequency) of an event gets closer and closer to the theoretical probability. In insurance, this translates to a better prediction of losses as the number of insured individuals increases, which allows insurers to set premiums that are sufficient to cover claims, company operating costs, and profits.
With large sample sizes, insurers can use this statistical principle to assess risk across different risk groups, ensuring actuarial fairness. To apply these probability laws effectively, insurers rely on the central limit theorem which reinforces the law of large numbers by stating the sample mean will get closer to the population mean as sample sizes increase.