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Difficulty: MediumLaw of Large Numbers

A group life insurance underwriter is evaluating a proposed policy that would cover 15,000 employees of a large national retailer. The employees share generally similar demographic and occupational risk profiles. Which of the following statements best describes how the Law of Large Numbers applies to this specific group life portfolio?

  1. It allows the insurer to accurately forecast the aggregate death claims for the entire group, even though predicting which specific employees will pass away remains impossible.Answer
  2. B
    It enables the underwriter to analyze the pooled demographic data and pinpoint exactly which individual employees will suffer a fatal event during the policy year.
  3. C
    It transforms the pure risk of human mortality into a speculative risk, ensuring that the collected premiums will mathematically result in a guaranteed financial gain.
  4. D
    It functions as a method of risk avoidance, eliminating the overall financial uncertainty of premature death by neutralizing the statistical chance of multiple simultaneous claims.

Answer

The statement accurately describing that the insurer can forecast aggregate death claims for the group, while individual outcomes remain unpredictable.
The correct statement perfectly captures the essence of the Law of Large Numbers in insurance. By pooling 15,000 similar exposure units, the insurer can rely on statistical probability to highly accurately predict the total number of mortality claims for the group. However, the fundamental nature of the risk means it remains entirely impossible to foresee exactly which specific employees will make up those aggregate claims.

Step-by-Step Solution

1
Analyze the scenario parameters.
The scenario involves a large number of homogeneous exposure units (15,000 employees with similar risk profiles).
Identifying the exposure units confirms that the core principles of the Law of Large Numbers apply.
2
Recall the definition and function of the Law of Large Numbers.
As the number of similar exposure units increases, the actual losses approach expected losses, making aggregate prediction highly accurate, but individual prediction remains impossible.
This is the foundational definition required to evaluate the given statements.
3
Evaluate the options against the core principle.
Only the option emphasizing accurate aggregate prediction combined with individual unpredictability matches the insurance concept.
Other options incorrectly assume individual prediction is possible, confuse pure with speculative risk, or misidentify risk transfer as risk avoidance.

Key Concept

Law of Large Numbers
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Topics

Law of Large Numbers

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