3.1.1随机事件的概率的Breamer(2018-03-22)

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 \title[随机事件的概率]{\Huge\bfseries 3.1. 随机事件的概率}
 
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 \begin{frame}
   \titlepage
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 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \begin{frame}{\Huge 第三章\quad 概率}
 \begin{figure}
 \vskip-.5em% \hskip-6em
 \includegraphics[page=,scale=0.60]{mindmap}
 \end{figure}
 \end{frame}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \begin{frame}{\Huge 概率论的由来}
 相传，两位著名的数学家Pascal和Fermat经常在巴黎的咖啡屋里碰面讨论深奥的数学问题，为了解乏，他们经常玩一个简单的游戏.
 \begin{figure}
 \includegraphics[scale=0.4]{paris}
 \end{figure}
 \end{frame}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \begin{frame}{\Huge 概率论的由来}
 重复抛掷硬币---每次正面朝上Pascal得一分，反面朝上Fermat得一分.一方先得三分，另一方就买单.\\\pause
 一天，他们抛掷一次硬币，出现正面朝上（Pascal得一分）, Fermat有急事必须离开. 之后他们就想应该由谁来买单呢？
  或者采用分摊，怎么分摊才合理呢？
 \end{frame}
 \begin{frame}{\Huge 3.1. 随机事件的概率}
 \begin{figure}
 \vskip-.5em% \hskip-6em
 \includegraphics[page=,scale=0.60]{mindmap}
 \end{figure}
 \end{frame}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \begin{frame}{\Huge 情景引入}
 有四张红色卡片，分别编号为1,,,，从中抽取一张卡片
  \begin{itemize}
 \item “抽到的卡片是红色的”
  \item “抽到的卡片是蓝色的”
 \item “抽到的卡片编号是1号”
   \end{itemize}
 \end{frame}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \begin{frame}{\Huge 事件的分类}
  \begin{itemize}\pause
 \item \alert{必然事件}：在条件S下，一定会发生的事件.\pause
     \item \alert{不可能事件}：在条件S下，一定不会发生的事件.\pause
     \item \alert{随机事件}：在条件S下，可能发生也可能不发生的事件.\pause
 \item {\centering 必然事件和不可能事件称为\alert{确定事件}.}\pause
 \item 确定事件和随机事件统称为\alert{事件},一般用大写字母$A,B,C$…表示.\pause
   \end{itemize}
 
 \end{frame}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \begin{frame}{\Huge 事件的分类 }
  判断下列事件哪些是必然事件，哪些是不可能事件，哪些是随机事件？\\
 %\begin{enumerate}
 ()“抛一块石头，下落”；\\
 ()“某人射击一次,中靶”;\\
 ()“从分别标有1,,,,5的5张标签中任取1张,得到4号签”;\\
 ()“掷一枚硬币,出现正面”;\\
 ()“没有水分,种子能发芽”;\\
 ()“在常温下,焊锡熔化”
 %\end{enumerate}
 \end{frame}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \begin{frame}{\Huge 随机事件的概率}
 对于随机事件，我们知道它发生的可能性的大小事非常重要的。那么我们用什么来度量随机事件发生的可能性的大小呢？\\ \pause
 \begin{block}{}
 用\alert{概率}度量随机事件发生的可能性大小.
   \end{block}\pause
 如何获得随机事件发生的概率？
 \end{frame}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \begin{frame}{\Huge 试验}
 第一步，全班同学各取一枚相同的硬币，做$$次抛硬币试验，每人记录下试验结果，填在下表中：\\
 \begin{center}
   \setlength{\extrarowheight}{.5mm}
   %\addtolength{\tabcolsep}{1mm}
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    \begin{tabular}{|c|c|c|c|}
      姓名         & 试验次数&正面朝上的次数&正面朝上的比例 \\\hline
            & &  & \\\hline
     \end{tabular}
  \end{center}
 {\Huge \bfseries 思考 } \quad 与其他同学的试验结果比较，你的结果和他们一致吗？为什么会出现这样的情况？
 
 \end{frame}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \begin{frame}{\Huge 试验}
 第二步，每个小组把本组同学的试验结果统计一下，填入下表：\\
 \begin{center}
   \setlength{\extrarowheight}{.5mm}
   %\addtolength{\tabcolsep}{1mm}
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    \begin{tabular}{|c|c|c|c|}
      组次        & 试验总次数&正面朝上的总次数&正面朝上的比例 \\\hline
            & &  & \\\hline
     \end{tabular}
  \end{center}
 {\Huge \bfseries 思考 } \quad 与其他小组的试验结果比较，各种的结果一致吗？为什么？
 \end{frame}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \begin{frame}{\Huge 试验}
 第三步，请一个同学把全班同学的试验结果统计一下，填入下表：\\
 \begin{center}
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    \begin{tabular}{|c|c|c|c|}
      班级        & 试验总次数&正面朝上的总次数&正面朝上的比例 \\\hline
            & &  & \\\hline
     \end{tabular}
  \end{center}
 \end{frame}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \begin{frame}{\Huge 试验}
 第四步，请把全班每个同学的试验中正面朝上的次数收集起来，并用条形图表示.\\
 \vskip6.5em
 {\Huge \bfseries 观察 } \quad 这个条形图有什么特点？
 
 \end{frame}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \begin{frame}{\Huge 试验}
 第五步，请同学们找出抛硬币时“正面朝上”这个事件发生的规律性.\\
 \vskip6.5em
 {\Huge \bfseries 探究 } \quad 如果同学们再重复一次上面的试验，全班的汇总结果还会和这次的汇总结果一致吗？如果不一致，你能说出原因吗？
 \end{frame}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \begin{frame}{\Huge 基本概念}
 \begin{block}{频数}
 在相同的条件$S$下重复$n$次试验，观察某一个事件$A$是否出现，称$n$次试验中事件A出现的次数$n_A$为事件$A$出现的频数.
   \end{block}\pause
 \begin{block}{频率}
 我们称事件$A$出现的比例$f_n(A)=\dfrac{n_A}{n}$为事件出现的频率.
   \end{block}
 \end{frame}
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \begin{frame}{\Huge 计算机模拟掷硬币试验}
 \begin{figure}
 \includegraphics[scale=0.25]{computer}
 \end{figure}\pause
 \begin{block}{}
 在大量重复试验后,随着试验次数的增加，“正面朝上”的频率
 \alert{逐渐稳定}在0.5的附近.
   \end{block}
 \end{frame}
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \begin{frame}{\Huge 历史上一些掷硬币的试验结果}
 \begin{center}
   \setlength{\extrarowheight}{.5mm}
   %\addtolength{\tabcolsep}{1mm}
   \rowcolors[]{}{orange!}{white!!gray}
    \begin{tabular}{|c|c|c|}
       试验次数&正面朝上的次数&正面朝上的比例 \\\hline
            & & 0.5181 \\
 &&0.5069\\
 &&0.5016\\
 &&0.5005\\
 &&0.4995\\
 &&0.5011\\\hline
     \end{tabular}
  \end{center}
 \end{frame}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \begin{frame}{\Huge 规律总结 }
 由以上试验的规律，得到在一般情况下随机事件A的规律：\\
  \begin{block}{}
 一般来说,在大量重复进行同一试验时,随着试验次数的增加,事件A发生的频率$f_n(A)=\dfrac{n_A}{n}$会逐渐稳定在区间$[,]$中的某个\alert{常数}上.\pause 这个常数叫做事件A的\alert{概率}，记作$P(A)$.\\
   \end{block}
   \begin{block}{大数定律}
 1713年，瑞士数学家雅各布·贝努利(Jacob Bernouli)对这一客观规律性从理论上给予了证明，并提出了著名的大数定律：\alert{随着试验次数的增加，频率稳定在概率附近.}.
   \end{block}
 \end{frame}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \begin{frame}{\Huge 例题 }
 例1 某运动员在同一条件下进行射击,结果如下表所示:
 \begin{center}
   \setlength{\extrarowheight}{.5mm}
   %\addtolength{\tabcolsep}{1mm}
   \rowcolors[]{}{orange!}{white!!gray}
    \begin{tabular}{|c|c|c|c|c|c|c|}
 射击次数$n$    &    &&    &    &    &    \\\hline
 击中靶心次数$n_A$&    &    &    &    &    &    \\\hline
 击中靶心的频率&&&&&&    \\\hline
     \end{tabular}
  \end{center}
 
  \begin{block}{}
 ()填写表中击中靶心的频率;
   \end{block}
   \begin{block}{}
 ()这个运动员射击一次,击中靶心的概率约是多少?
   \end{block}
 \end{frame}
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \begin{frame}{\Huge 小组讨论}
 %\Lauge
 
  \begin{itemize}
     \item 事件$A$发生的\alert{频率}是不是不变的？
     \item 事件$A$发生的\alert{概率}是不是不变的？
 \item 它们之间有什么\alert{区别与联系}？
   \end{itemize}
 \end{frame}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \begin{frame}{\Huge 区别与联系}\pause
 
   \begin{block}{区别：}
 频率本身是随机的,在试验前不能确定,做同样次数或不同次数的重复试验得到的事件的频率都可能不同.而概率是一个确定数,是客观存在的,与每次试验无关.
   \end{block}\pause
 
   \begin{block}{联系：}
 随着试验次数的增加, 频率会在概率的附近摆动,并趋于稳定.在实际问题中,若事件的概率未知,常用频率作为它的估计值.
   \end{block}
 \end{frame}
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 \begin{frame}{\Huge 作业}
 \Huge 课本P113练习1，
 \end{frame}
 
 \begin{frame}{}
   \begin{center}
     \begin{tikzpicture}
       \node[above,xscale=1.2,yscale=1.4]{\Huge\bfseries 谢谢!};
       \node[xscale=1.2,above,yscale=-1.4,scope fading=south,opacity=0.2]{\Huge\bfseries 谢谢!};
     \end{tikzpicture}
   \end{center}
 \end{frame}
 
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