# 概率论与数理统计在生活及教学中的应用Probability Theory and Mathematical Statistics Apply in the Life and Teaching

DOI: 10.12677/AAM.2018.710148, PDF, HTML, XML, 下载: 801  浏览: 5,358

Abstract: In real life, many problems can be solved through knowledge of probability theory, such as insurance industry, lottery industry and teaching process. In this paper, we mainly use some cases to show the importance of probability theory in practical applications and then give a brief calculation process. The paper also briefly summarizes teaching process for solving probability problem.

1. 引言

2. 股票投资

$P\left(A\right)=0.8,P\left(B\right)=0.6,P\left(C\right)=0.5.$

$\begin{array}{c}P\left(AB+AC+BC\right)=P\left(AB\right)+P\left(AC\right)+P\left(BC\right)-2P\left(ABC\right)\\ =P\left(A\right)P\left(B\right)+P\left(A\right)P\left(C\right)+P\left(B\right)P\left(C\right)-2P\left(A\right)P\left(B\right)P\left(C\right)\\ =0.8×0.6+0.8×0.5+0.6×0.5-2×0.8×0.6×0.5=0.7.\end{array}$

$\begin{array}{c}P\left(A+B+C\right)=P\left(A\right)+P\left(B\right)+P\left(C\right)-P\left(AB\right)-P\left(AC\right)-P\left(BC\right)+P\left(ABC\right)\\ =0.8+0.6+0.5-0.8×0.6-0.8×0.5-0.6×0.5+0.8×0.6×0.5=0.96.\end{array}$

3. 随机事件与保险

$\begin{array}{l}p\left(x=k\right)={C}_{15}^{k}×{0.2}^{k}×{0.8}^{15-k},k=0,1,2,\cdots ,15.\\ p\left(x=3\right)={C}_{15}^{3}×{0.2}^{3}×{0.8}^{12}=0.2501.\\ p\left(x\ge 2\right)=1-p\left(x=1\right)-p\left(x=0\right)=0.8329.\end{array}$

4. 极限计算中的应用

$\underset{a\to \infty }{\mathrm{lim}}\frac{{6}^{a}}{a!}$ 的极限。

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