Final answer:
The law of large numbers is crucial for the predictability required in insurance to align the experimental probability with the theoretical probability, allowing for financially stable insurance operations.
Step-by-step explanation:
The law of large numbers is necessary for insurance because it ensures that the experimental probability of an event (what actually happens) aligns closely with the theoretical probability as the number of insured events increases. This principle allows insurance companies to predict and cover 1) the average person's claims, 2) the costs of running the company, and 3) still have room for profit. The law of large numbers, in conjunction with the central limit theorem, clarifies that as more people are insured (larger sample size), the more predictable the outcomes become, allowing for the calculation of premiums that are fair and ensure the financial stability of the insurance firm.