Question

In an insurance system, would you expect each person to receive in benefits pretty much what they pay in premiums or is it just that the average benefits paid will equal the average premiums paid?

Short answer

In an insurance system, each person's benefits and premiums may not necessarily be equal, as they depend on various factors such as age, health, and risk assessment. However, the average benefits paid across all policyholders will usually equal the average premiums paid due to the law of large numbers, which allows the insurance company to manage risk and maintain financial stability.

Step-by-step solution

Introduction to Insurance System

Insurance is a system where people or organizations protect themselves from financial losses by transferring the risk to an insurance company. The company collects premiums from policyholders, and in return, it provides financial assistance in case of a covered event, such as accidents, illnesses, or property damages.

Individual Benefits and Premiums

In an insurance system, each person's benefits and premiums may not necessarily be the same. There are several factors that can influence an individual's premiums, such as age, health, occupation, and other risk factors. The insurance company estimates the likelihood of a covered event based on these factors and charges the person accordingly. On the other hand, benefits received depend on the circumstances leading to the claim. A person may receive benefits greater than the premiums paid if they experience a costly covered event, or they may receive no benefits at all if they never experience such an event.

Average Benefits and Premiums

While each person may not receive benefits equal to the premiums they pay, the average benefits paid across all policyholders will usually equal the average premiums paid. The reason for this is the law of large numbers, which states that as the number of policyholders increases, the average benefits and premiums will converge. This allows the insurance company to manage the risk and maintain financial stability while providing coverage to its policyholders. In summary, while each individual may not receive benefits equal to their premiums paid, the average benefits and premiums paid in an insurance system will typically balance out. This is due to the pooling of risk and the law of large numbers at work in the insurance industry.