What is Law of Large Numbers ?

Law of Large Numbers is a principle of probability according to which the frequencies of events with the same likelihood of occurrence even out, given enough trials or instances. As the number of experiments increases, the actual ratio of outcomes will converge on the theoretical, or expected, a ratio of outcomes. For example, if a fair coin is tossed 1,000,000 times, the heads-to-tails ratio will be extremely close to 1:1. However, if the same coin is tossed only 10 times, the ratio will likely not be 1:1. The law of large numbers is sometimes referred to as the law of averages and generalized, mistakenly, to situations with too few trials to illustrate the law of large numbers. This error in logic is known as the gambler’s fallacy. If for example, someone tosses a fair coin and gets several heads in a row, that person might think that the next toss is more likely to come up tails than heads because they expect frequencies of outcomes to become equal. But, because each coin toss is an independent event, the true probabilities of the two outcomes are still equal for the next coin toss and any coin toss that might follow.

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