Match each scenario or concept related to the Law of Large Numbers with its correct statistical or actuarial outcome.
- Increasing the number of similar homes in a property insurance poolImproves the insurer's ability to accurately predict total aggregate losses for the group
- Attempting to predict if a specific, individual homeowner will suffer a fire lossRemains entirely impossible and uncertain, regardless of how large the group becomes
- Combining personal auto risks and commercial aviation risks into the exact same calculation poolViolates the requirement that risks must be homogeneous exposure units
- The primary actuarial benefit of applying the Law of Large NumbersAllows the insurer to charge stable, adequate premiums based on highly predictable group outcomes
Answer
Increasing the pool size matches with improving aggregate predictions. Individual prediction matches with remaining impossible. Combining different risks matches with violating homogeneous units. The primary benefit matches with allowing stable premium pricing.
The correct matches directly align the theoretical rules of the Law of Large Numbers with their practical underwriting outcomes. A larger pool of similar risks increases aggregate predictability, which enables stable pricing. However, the exposure units must be homogeneous, and the statistical law never provides predictive power for a single individual's future.
Step-by-Step Solution
Key Concept
The Law of Large Numbers improves overall group predictability when using homogeneous units, but it cannot predict individual losses.