生活中的一些概率问题

摘 要

随着科学技术的迅速发展和计算机的普及应用，概率论正广泛的应用到各个行业，它与我们的生活密切相关.在我们的生活中，有许多问题都可以直接或间接的利用概率论来解决.本文从概率论的基础出发，通过在日常生活中包括生日缘分、博彩、抽奖、比赛等以及商品买卖与贮存和其他一些特殊的例子来说明概率论的重要性.

关键词：概率论、生日缘分、博彩、比赛、商品买卖与贮存.

Abstract

With the rapid development of science and technology and the popularization

of computer applications, probability theory is widely applied to various industnss, it is closely related to our lives. In our lives, there are many problems can be directly or indirectly, the use of probability theory to resolve. In this paper, probability theory, basis, by fate in their daily lives, including birthdays, gaming, sweepstakes, contests, etc. as well as commodity trading and storage and some other specific examples to illustrate the importance of probability theory.

Key word: Probability theory, birthday fate, gaming, competition, commodities trading and storage.

目 录

一、引言

二、概率论的介绍

（一）定义·······························································································(01) （二）基本理论与方法···········································································(01) （1）古典概率·················································································(01)

（2）条件概率·················································································(02) （3）离散型随机变量·····································································(02) （4）连续型随机变量及其密度函数·············································(03) （5）大树定律及中心极限定理·····················································(03)

三、概率论的应用

（一）生日缘分·······················································································(04) （二）博彩·······························································································(04) （三）抽奖·······························································································(06) （一）比赛·······························································································(08) （一）商品贮存于买卖···········································································(09) （一）其他一些例子···············································································(12)

四、总结

·······································································································(13)

参考文献 ··················································································· (14) 致谢 ··························································································· (15)

浅析生活中的一些概率问题

一、引言

概率论是一门相当有趣的数学分支，它所研究的内容一般包括随机事件的概率、统计独立性和更深层次上的规律性.“概率”是现行告知和哪个数学大纲中的必修内容，概率最早起源于对赌博问题的研究，十七世纪帕斯卡、惠更斯等数学家对“合理分配赌注”问题进行了深入广泛的研究，并作了系统的归纳总结，于是便出现了概率论，随着社会的发展，概率论在工农业生产、国名经济、现代科学技术等方面具有广泛的应用，在日常生活中，概率论的应用更是普遍，几乎无处不在，本文从生日缘分，博彩，抽奖，比赛，商品贮存等方面举例说明概率论在生活中的重要应用.让人们更深刻的了解概率论与生活的密切联系.

二、概率论的介绍

（一）、定义

概率论与数理统计是数学的一门分支.在自然现象和社会现象中，有一些现象就其个别来说是无规则的，但是通过大量的试验和观察以后，就其整体来说却呈现出一种严格的非偶然的规律性.这些现象称为“随机现象”.概率论就是研究这种“随机现象”规律性的一门学科. （二）、基本理论与方法 （1） 古典概率；

在古代较早的时候，在一些特殊情形下，人们利用研究对象的物理或几何性质所具有的对称性，确定概率的一种方法如下：

对于某一随机试验，如果它的全体基本事件E1,E2,...,En是有穷的，且具有等可能性，则对任意事件A，对应的概率P(A)由下式计算：

P(A)?并把它称作古典概率.

事件A包含的基本事件数（k）

基本事件总数（n）

（2）条件概率；

在实际问题中，一般除了要考虑事件A的概率P(A)，还要考虑在“已知事件B已发生”这一条件下，事件A发生的概率，一般地说，后者发生的概率与前者的概率未必相同.为了区别起见，我们把后者叫作条件概率，记为P(AB)或

PB(A)，读作在条件B下，事件A的条件概率.

条件概率的定义：

定义1. 4. 1 设(?,?,P)为一概率空间，A??，B??，且P(B)>0，在“已知事件B已经发生”的条件下，“事件A发生”的条件概率P(AB)定义为：

P(AB)?由条件概率的定义可得：

P(A?B)

P(B)P(AB)?P(AB)P(B) P(AB)?P(BA)P(A)

定理 1. 4. 1 （全概率公式）

?的一个有穷部分，且 设(?,?,P)为一概率空间，A1,A2,...,An是

P(Ai)>0(i?1,2,3,...,n).则对于与A1,A2,...,An中的每一个发生有关的事件B??，有

P(B)??P(BAi)P(Ai)

i?1n式称为全概率公式. （3）离散型随机变量；

定义2. 1. 2 设?为离散型随机变量，亦即?的一切可能值为x1,x2,...xn,...记

pn?P(??xn)(n?1,2,...)，称p1,p2,...,pn,...为?的分布列，亦称为?的概率

函数.

由上述可知，若?为随机变量，则Pn有意义.

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