Bhaskar and Fermat are two great French mathematicians.
Pascal knew two gamblers and they asked him a question. They said that after they made a bet, 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?
Divide the money into seven parts, right? He who wins four games gets four, and he who wins three games gets three. 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 the probability of winning or losing is 1/2, so the money he takes should be1/2×1+1/2 = 3/4. Of course, b should get 1/4.
Through this discussion, an important concept in probability theory-mathematical expectation began to take shape. Mathematical expectation is an average value, that is, there is a systematic algorithm for how to calculate the uncertain money in the future today. This is a probability of winning or losing 1/2 multiplied by the money he may get, and then add them up.
Probability theory has developed since then, and today it has become a very widely used subject.
Probability and "knowledge of gamblers"