The more an event is repeated, the more predictable the outcome becomes. This is an example of

Rationale

The law of large numbers.

This statement refers to a fundamental principle in probability and statistics, stating that as the sample size of repeated events increases, the average or expected outcome tends to converge towards the theoretical or expected value. Essentially, this law highlights the trend of outcomes becoming more stable and predictable with a larger number of trials.

A (the law of large numbers.) CORRECT

The law of large numbers precisely encapsulates the scenario described, where repeated trials lead to a convergence towards the expected outcome. It is a foundational concept in probability theory, emphasizing the stability and predictability of outcomes with increased sample sizes.

B (standard deviation.) YOUR ANSWER

Standard deviation measures the dispersion or spread of data points around the mean in a dataset. While it is related to variability, it does not directly address the predictability of outcomes based on the number of repetitions, making it an incorrect choice in this context.

C (average dispersion.) YOUR ANSWER

Average dispersion is not a recognized statistical concept. While dispersion refers to the spread of data points, there is no standard term or principle known as "average dispersion" in statistical analysis.

D (normal variance.) YOUR ANSWER

Normal variance does not align with the scenario presented in the question. Variance typically refers to the average squared deviation of data points from the mean, a measure of data variability that does not directly relate to the predictability of outcomes with repeated events.

Conclusion

The law of large numbers accurately captures the essence of the statement that repeated events lead to more predictable outcomes. This principle underpins the stability and reliability of statistical predictions as sample sizes increase, showcasing the fundamental relationship between repetition and outcome predictability in probability theory and statistical analysis.

The more an event is repeated, the more predictable the outcome becomes. This is an example of

The law of large numbers.

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