The law of the great numbers was formalized at the 17th century at the time of discovered new mathematical languages.

Primarily, the law of the great numbers indicates that when one makes a random pulling in a series of big size, more one increases the sample size, more the characteristic statistics of pulling (the sample) approach the statistical characteristics of the population. But it is interesting to note that the sample size to take to approach the characteristics of the initial population depends only slightly even at all on the size of the initial series: for a survey with the Luxembourg or the the United States, it is enough, to obtain an equal precision to take an of the same sample cuts.

It is on this law which rest the majority of the Sondage S. They question a sufficiently significant number people to know the opinion (probable) of the whole population. In the same way, without the formalization of the law of the great numbers, the Assurance could never have developed with such a rise. Indeed, this law makes it possible to the insurers to determine the probabilities that the disasters of which they are guaranteeing will realize or not.

The law of the great numbers is also useful in inférentielle statistics, to determine a law of probability starting from a series of experiments.

The mathematicians distinguish two statements, respectively called weak law of the great numbers and strong law of the great numbers .

It is interesting to note that the law of the great numbers raises a metaphysical question of order: nobody is astonished that events considered in an isolated way are subjected to the Hasard (it is not impossible to obtain 1000 times crushes while launching a coin 1000 times…). And yet, if the experiment is made, it is noted that there is no total chance (approximately one obtains 50% of pile and 50% of face…), as if there was a natural law of balance, as if the chaos were impossible and the improbable Catastrophe S…

One should not however not confuse the average of the profits and the absolute profit. If two players play pile very a long time or face, that which loses giving one Euro to that which gains, the average of the profits of each player will tend indeed towards the 0 (average being defined like: the profit divided by the number of played parts), but the profit of each player will pass alternatively by tops and bottoms of increasing amplitude.