摘要：本文选择了在当下比较流行的乐透型彩票作为研究对象, 又从中选取了 2 种 具体的彩票类型：双色球和“N 选 M”, 首先对两种彩票的游戏规则、中奖条件和 奖金分配做了简单介绍和具体说明. 根据其游戏规则可明显看出这两种都可看 作是古典概型. 其次针对“双色球”, 先从数学的角度上用所学的概率论与统计学 知识对其理论上各奖级的中奖概率进行了计算与分析, 然后运用数学软件 MATLAB, 使用纯随机数法的算法对双色球的开奖过程进行了模拟, 先随机产 生 n 组随机号码, 再随机产生规定的中奖号码, 然后计算中奖概率, 最后与理论 中奖的概率进行对比分析. 针对“N 选 M”, 先利用数学知识对其理论中奖概率进 行了分析, 继而选择了其中一种具体玩法：“22 选 5”, 利用前面的理论结果进行 了具体示例分析. 在此过程中, 发现实验中所得到的结果与真实结果均较为符合, 由此可判断本文所使用的检测方法较为合理. 论文最后, 尝试建立了一个彩票的 评价准则, 对本文所研究的两种彩票做了排序, 希望可以用来对其它不同的彩票 进行一定的评估,  为彩民选购彩票时做一定的参考.

关键词：彩票 古典概型 中奖概率 纯随机数法 卡方拟合优度检验

Analysis and Comparison of the Winning Probability of bichromal Ball and " N-choose M " Lottery

Abstract：In this paper, the most popular Lotto-type lottery ticket is selected as the research object, and two specific types of lottery tickets are selected: bichromal ball and N-choose M as research objects. First, a brief introduction and specific explanation of the game rules, winning conditions and bonus distribution of the two lottery tickets are given. Secondly, aiming at bichromal spheres, mathematical probability is used to calculate and analyze the winning probability of each prize level theoretically based on the learned probability theory and statistical knowledge. Then the mathematics software MATLAB is used, and the algorithm using pure random numbers is used for bichromal spheres. The lottery process was simulated. Randomly generate n sets of random numbers, randomly generate the specified winning numbers, and then calculate the winning probability. Finally, compare and analyze the probability of the theoretical winnings. For N-choose M, we first use mathematical knowledge to analyze its theoretical winning probabilities, including  model assumptions, single-note winning probability analysis, parity analysis, span analysis, sum-value analysis, and odd number distribution under the condition of span determination. Span and odd number of joint distribution. Then choose one of the specific gameplay: 22 choose 5, using the previous theoretical results for a specific example analysis. At last, the thesis tries to establish a lottery ticket evaluation criterion, sorts the two lottery tickets studied in this paper, and hopes to use it to evaluate  certain  other lottery tickets.

Keywords: Lottery ticket classical models of probability Winning probability Pure random number method Chi-square goodness-of-fit test

目录

双色球和“N 选 M”彩票的中奖概率分析与比较 3

摘要 3

Abstract 4

一、 前言 1

1.1 相关背景 1

1.2 彩票简介 1

1.2.1 乐透型彩票 1

1.2.2 双色球