When it comes to the story of the origin of probability theory, we should mention two French mathematicians. One is Pascal and the other is Fermat. Pascal was a famous "child prodigy" mathematician in17th century. Fermat is an amateur mathematician, and many stories are related to him.

Pascal Fermat

Pascal's two friends are gamblers.

165 1 year, a French aristocrat, Mele, asked Pascal, a French mathematician and physicist, a very interesting question of "dividing bets". The two gamblers said that after placing their bets, it was agreed that whoever won the first five games would get all the bets. After gambling for a long time, A won four games and B won three. It's getting late, and they don't want to gamble any more. So, how should this money be divided? Do you divide the money into seven parts, four for those who win four games and three for those who win three games? Or because the first time I said five innings, no one arrived, so one person got half?

Neither of these points is correct. The correct answer is: the person who wins four games gets 3/4 of the money, and the person who wins three games gets 1/4 of the money.

Why? Suppose the two of them bet another game, and either A wins or B wins. If A wins five games, all the money should go to him. If A loses, that is, A and B win four games each, and the money will be divided equally. Now A's winning or losing probability is 1/2, so his money should be 1/2×1/2×1/2 = 3/4. Of course, B should get1.

This question stumped him. He thought hard for two or three years until 1654. So he wrote to his good friend Fermat, and they discussed the results and reached a consensus: Mailer's division was correct, he deserved 64 gold coins, and gamblers deserved 64 gold coins.

Through this discussion, an important concept in probability theory-mathematical expectation began to take shape.

Among the above problems, mathematical expectation is an average, that is, how to calculate the uncertain money in today's future. This requires multiplying the money that A may get by the winning or losing probability of 1/2, and then adding them up. Probability theory has developed since then, and today it has become a very widely used subject.

At this time, a Dutch mathematician Huygens heard the news in Paris and took part in their discussion. As a result of the discussion, Huygens wrote a book called Calculation in Gambling (1657), which is the earliest work of probability theory.

Probability theory has now become an important branch of mathematics, which is widely used in various fields of science and technology.

Further development of probability theory

After Pascal, Fermat and Huygens, the first person who paid serious attention to probability theory was Jacob? Bernoulli's book Guessing contains the narration of the law of large numbers; De moivre first used the normal distribution curve; Lagrange's contribution lies in the error theory.

However, it was Laplace who first established probability theory on a solid mathematical basis. Since 177 1, Laplace has published a series of important works, especially "The Theory of Probability Analytics" published by 18 12, which has made a powerful mathematical synthesis of classical probability theory and described and proved many important theorems. Laplace's works also discuss the application of probability theory in demography, insurance, weights and measures, astronomy and even some legal issues. In the18th century, probability theory is no longer a subject only related to gambling.