South Carolina Personal Lines Practice Exam

According to the law of large numbers, which scenario is more predictable?

1. A smaller group with diverse exposures

2. A larger group with similar exposures

3. An individual with unique exposures

4. A small random sample of exposures

The correct answer is: A larger group with similar exposures

The law of large numbers states that as the number of trials or observations increases, the average of the results will get closer to the expected value. This principle is foundational in fields such as insurance, where it helps predict loss and premium calculations. In the context given, a larger group with similar exposures is more predictable because the similarity in exposures reduces variability among the individual outcomes. When many individuals share similar risk characteristics, it becomes easier to estimate expected losses accurately, as any anomalies or outliers among individual cases tend to cancel each other out when viewed collectively. In contrast, smaller groups with diverse exposures introduce more unpredictability, as the variances in risks can skew the results significantly. An individual with unique exposures is particularly unpredictable since their risk factors do not benefit from the averaging effect found in larger groups. Lastly, a small random sample may not sufficiently capture the underlying trends needed for accurate predictions, as the randomness and small size can lead to considerable fluctuations, thus reducing reliability.