Question

What is the law of large numbers? Why do insurers rely on the law of large numbers?

a) The law stating that larger risks lead to larger losses; insurers rely on it for risk assessment.

b) The law stating that as the number of exposure units increases, the more closely the actual loss experience will approach the expected loss experience; insurers rely on it for more accurate predictions.

c) The law stating that only large insurers can accurately predict losses; insurers rely on it for financial stability.

d) The law stating that losses are random and unpredictable; insurers rely on it for flexibility.

Answer 1

Answer: The correct answer is B

Step-by-step explanation:

The law stating that as the number of exposure units increases, the more closely the actual loss experience will approach the expected loss experience; insurers rely on it for more accurate predictions.

The law of large numbers is a statistical principle that states that as the number of observations or exposure units increases, the more accurate the predictions or estimates will be. Insurers rely on this principle because they deal with a large number of policies and exposure units, and by using the law of large numbers, they can make more accurate predictions about the likelihood of losses occurring and the amount of losses they may face. This allows insurers to price their policies more accurately and manage their risks more effectively.

Answer 2

The law of large numbers indicates that as sample size increases, the experimental results approach the theoretical probability. Insurers depend on this principle to accurately predict losses, because it leads to the actual loss experience reflecting the expected loss experience more reliably with a larger number of exposure units.

Step-by-step explanation:

The law of large numbers is a fundamental principle in probability and statistics, which states that as the number of trials or samples increases, the actual or experimental frequency of outcomes will converge on the theoretical or expected frequency of those outcomes. In other words, the more times an experiment is conducted, or the more data points you collect, the closer the calculated results (the relative frequency) will be to what is expected theoretically (the theoretical probability).

Insurers rely on the law of large numbers to make more accurate predictions regarding potential losses. This principle allows for a more precise assessment of risk because it posits that with a larger amount of exposure units, the observed loss experience will mirror the expected loss experience more closely. Therefore, the correct answer to the student's question is b) The law stating that as the number of exposure units increases, the more closely the actual loss experience will approach the expected loss experience; insurers rely on it for more accurate predictions.