彩票中的数学

本模型讨论的是如何评判传统型彩票和乐透型彩票的一般评奖方案的合理性问题。本文首先根据彩票中奖规 则,利用古典概率求出了这两种类型彩票的各种奖项出现的可能性。把每注彩票中奖与否看成贝努利试验,在 假设每期彩票的销售量足够多的前提下,由贝努利大数定律归结为正态分布,从而求出了每注彩票的平均收益 率。在此基础上,结合公平尺度,利用彩民的博彩心理因素构造了评判方案合理性的判别函数,利用MATLAB6 1软件编程计算,判别出题目所给方案的奖金设置的优劣,并且利用这个判别函数,我们建立了求解最优方案的 非线性规划模型。通过求解所建立的模型,找到在给定销售注数下最优方案及奖项和奖金额的设置。

Mathematics in Lottery

This model discusses how to evaluate the rationality of the general prize-winning evaluatityt procedures on the traditional lottery and lotto. First, according to the prize-winning rules, this paper found the probability of the various awards cases of two types by the use of the classical probability. Regarding each event of prizing-wining as Benouli experiment, under the assumption of the sufficient sales volume in each issue, and then whether each lottery ticket wins the prize or not, according to the Large-Number Law, is attributed to the Normal Distribution, and find the rate of return of each lottery ticket. On the basis of those efforts, we construct the function to evaluate the rationality of those programs with fair measure by taking advantage of the gambling mentality. In succession, by the use of Matlab 6.1, we calculated the model of Nonlinear planning on these questions. By the solution of the model, we find the optimal program for the given lottery sales volume and the settings of award items and prize amount.