# Law of Large Numbers - Explained

What is the Law of Large Numbers?

# What is the Law of Large Numbers?

This is a concept of probability denoting that the prevalence of events with a similar chance of occurrence eventually level out over a number of enough trials. As the number of instances continues to increase, the actual ratio of outcomes intersects at the theoretical or expected ratio of outcomes. This law outlines that the larger the sample size, the closer the mean is to the average of the total population. It was developed to address the fact a rapidly growing large entity can't keep the stride over a long time.

Back to: RESEARCH, ANALYSIS, & DECISION SCIENCE

## How does the Law of Large Numbers Work?

For example, assume a coin is tossed a million times, it is safe to say that the approximately half the tosses will be heads and half will be tails. Therefore, this ratio will be almost 1:1. When the coin is tossed twenty times, the ratio will be differing and might be 3:7 or any other. This law is sometimes misapplied to situations with very few experiments, and it results to an error in logic referred to as the gambler's fallacy. The law of large numbers, also known as the law of averages, is a theory used to explain the results arising from conducting a similar experiment many times. It states that the statistical probability of a sample with a specific value edges closer to the statistical probability of a collection of samples in the universe as the sample increases. Political polls use this method, and that's why they become more accurate the larger their sample size gets. Back in July 2015, Wal-Mart Stores Inc. generated an income of \$485.5 billion, and Amazon made \$95.8 billion. For them to increase their income by 50% based on this numbers, Walmart would require a total of \$242.8 billion, and Amazon would need just \$47.9. According to the law of large numbers, this increase would be more difficult for Walmart than for Amazon. This law assures stable long-term results for the averages of various random events and is therefore very essential.