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Achieving a sufficiently random selection of risks in an insurance pool is crucial for maintaining the stability and profitability of an insurer. A diverse range of risks ensures that no single type of risk disproportionately affects the overall pool. When risks vary widely, the insurer can better predict overall losses because different types of risks will behave differently under similar circumstances.

For example, if an insurance pool only includes high-risk individuals, the potential for high claims increases, which can threaten the financial health of the insurance company. Conversely, including a variety of low-risk individuals can help offset those higher costs. Thus, incorporating diverse types of risks—such as those from different geographical locations, age groups, or occupations—creates a balance that aids in risk assessment and pricing strategies.

The other options, while relevant to the operations of an insurance pool, do not directly address the necessity of randomness in risk selection. A large number of insured individuals can certainly help achieve statistical significance, but without diversity, the pool becomes biased toward certain types of risks. High policy limits and low premiums, while important for attracting customers, are secondary factors that do not inherently contribute to the randomness and diversity of risk selection within the pool itself.