What is the law of large numbers in probability?

The law of large numbers in probability states that as the number of trials increases, the experimental probability approaches the theoretical probability.

The law of large numbers is a fundamental concept in probability theory. It states that as the number of trials increases, the experimental probability of an event approaches the theoretical probability of that event. In other words, the more times an experiment is repeated, the closer the results will be to the expected outcome.

For example, if a fair coin is flipped 10 times, the theoretical probability of getting heads is 0.5. However, the experimental probability may be different due to chance. If the coin is flipped 100 times, the experimental probability will be closer to 0.5, and if it is flipped 1000 times, the experimental probability will be even closer.

The law of large numbers is important because it allows us to make predictions about the likelihood of an event based on theoretical probabilities. It also helps us to understand the concept of randomness and how it can affect the outcome of an experiment.

In summary, the law of large numbers in probability is a fundamental concept that states that as the number of trials increases, the experimental probability approaches the theoretical probability. This concept is important in understanding probability and making predictions about the likelihood of an event.