What is the Law of Large Numbers?

The Law of Large Numbers states that as the number of trials in an experiment increases, the experimental probability of an event will approach the theoretical probability of that event. This concept is fundamental in probability and statistics. It illustrates how random events, when occurring over a large number of trials, produce results that are more stable and closer to expected theoretical outcomes.

When conducting experiments with a limited number of trials, the results can vary significantly from the theoretical probabilities due to random fluctuations. However, as you increase the number of trials, those fluctuations tend to average out. This convergence means that the observed frequency of events becomes more reliable and reflects the theoretical probability more accurately.

This principle is crucial for various applications in business and social sciences, as it reinforces the accuracy of forecasting and decision-making based on empirical data. Understanding this law allows individuals to appreciate the importance of larger sample sizes in obtaining reliable statistical conclusions.

The other options do not accurately describe the Law of Large Numbers. For example, the idea that experimental probability will differ from theoretical probability as trials increase contradicts the law itself. Additionally, the law does not pertain solely to dependent events, nor does it specifically address the summation of probabilities in a strict sense.