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  • General

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  • 简单事件树图图

    In This Lesson
    ::在本课程中

    Y ou will use a tree diagram to organize outcomes . First, the process will be applied to simple events . A simple event is when there is one experiment at a time , and t herefore one set of outcomes.  Here is a tree diagram for flipping a coin:
    ::您将使用树图来组织结果。 首先, 此进程将应用到简单的事件。 一个简单的事件是当每次有一个实验时, 并且因此有一组结果。 这是用于翻转硬币的树图 :

    Tree diagram illustrating outcomes of flipping a coin, showing Heads and Tails with probabilities.
    Tree diagram for a single coin flip

    The outcomes are at the end of the branches, and the probabilities are written along the branch.  
    ::结果在分支的末尾,概率在分支上书写。

    If you were rolling a die, then there would be 6 branches, all with 1/6 for the probability and then 1, 2, 3, 4, 5, and 6 at the end of each branch. 
    ::如果你是滚动死亡, 那么会有6个分支, 所有的概率为1/6, 然后1, 2, 3, 4, 5, 6, 在每个分支的末端。

     

    Weather Predictions
    ::天气预报

    On an average summer day, in an average California town, the likelihood of rain is 3%, the likelihood of cloud coverage is 8%, and  sunny  the rest of the time. In the fall, the likelihood of rain increases to 22%, clouds 15%, and  sunny the rest of the time. In the winter, the likelihood of rain is 28%, clouds is 24%, snow is 2%, and  sunny the rest of the time.
    ::平均夏日,平均加利福尼亚镇的降雨概率为3%,云覆盖的可能性为8%,余下时间为阳光明媚。 秋天,雨的可能性增至22%,云层增加15%,余下时间更是阳光明媚。 冬季,雨的可能性为28%,云层为24%,雪为2%,余下时间则更是阳光明媚。

    Create three tree diagrams to represent these three different seasons  in this California town.  Type in the chance of each type of weather (as a decimal) above each branch and the type of weather at the end of the branch.  Each tree  is already labeled with each season.
    ::创建三个树图以代表这个加利福尼亚镇的这三个不同季节。 在每一分支上方的每种天气( 小数点)和树枝末端的天气类型中, 输入每棵树的机率( 小数点) 。 每棵树已经被标记为每个季节 。

     

     

    INTERACTIVE
    Weather Predictions with Tree Diagrams
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    In the Summer the likelihood of rain, clouds or sun is 3%, 8% and 89% respectively.
    In the Fall the likelihood of rain, clouds or sun is 22%, 15% and 63% respectively.
    In the Winter the likelihood of rain, clouds, snow or sun is 28%, 24%, 2% and 46% respectively.
    ::在夏季,雨、云或太阳的可能性分别为3%、8%和89%。 在秋季,雨、云或太阳的可能性分别为22%、15%和63%。 在冬季,雨、云、雪或太阳的可能性分别为28%、24%、2%和46%。

    • Type the numbers from above as decimals into the white boxes to create three tree diagrams.
      ::将以上数字作为小数输入到白框中,以创建三个树形图。
    • Select the corresponding season from the dropdown menu.
      ::从下调菜单中选择相应的季节 。
    • Each tree is already labeled with each season.
      ::每棵树已经贴上每一季的标签
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    Discussion Question
    ::讨论问题

    Why do you think temperature is not included? 
    ::为什么你认为温度不包括在内?

     

    The previous interactive is an example of an event where all of the outcomes had different probabilities of occurring. What if the outcomes had the same likelihood and there were a few different options?  In the next interactive, you will determine how many possible outcomes there are when different options are involved.
    ::上一次互动是一个事件的例子,其中所有结果的发生概率都不同。 如果结果具有同样的可能性,并且有几种不同的选择呢? 在下一次互动中,当涉及到不同的选择时,你将决定有多少可能的结果。

     

    How Many Outfits? 
    ::多少钱?

    Liz is starting a new job and she needs to buy some new clothes. In order to  be as efficient as possible with  her money, she decides to mix and match what she buys to create different outfits. If she buys 3 tops (green, orange, purple), 3 pairs of pants (black, brown, and blue) and 2 pairs of shoes (red and white), how many different outfits could she have?
    ::利兹正在开始新的工作,她需要买一些新衣服。 为了尽可能有效地利用她的钱,她决定混合和匹配她买的东西来制造不同的服装。 如果她买三顶(绿色、橙色、紫色)、三双裤子(黑色、棕色和蓝色)和两双鞋子(红白),她能穿多少不同的衣服?

    Use the interactive to drag each item of clothing  into  a tree diagram . 
    ::使用交互式工具将每件服装拖放到树形图中。

    Start with shirts in the first blank, pants at the end of the first branch (second blank), and shoes at the end of the second branch (third blank). You will use the pants and shoes several times.
    ::从第一个空白的衬衫开始,第一个空白处的末端的裤子(第二个空白)开始,第二个空白处的末端的鞋子(第三个空白)开始。你将数次使用裤子和鞋子。

     

     

    INTERACTIVE
    How Many Outfits?
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    • Click the button to add a tree.
      ::单击按钮添加树。
    • Use the dropdown menu to fill out a tree of different combination of outfits. More branches will appear as you fill out the tree.
      ::使用下拉菜单填满不同组合的树。 在您填满树时, 将会有更多树枝出现 。
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    Make  Your   Own Tree Diagram 
    ::制作您自己的树图图

    Pick a city in the US and determine the weather changes for each season.  Create your own tree diagram for each season (spring, summer, fall, winter).  Cite the website you used as well as the data range (last season/year, one year, 2 + years, etc).  Then, make a prediction based on these diagrams.  Be sure to include a title with the city name, centered at the top of the page.
    ::在美国选择一个城市, 并确定每个季节的天气变化 。 为每个季节( 春季、 夏季、 秋季、 冬季) 创建您自己的树图 。 请访问您使用的网站以及数据范围( 最后一个季节/ 年、 一年、 2+ 年等 ) 。 然后, 根据这些图表做出预测 。 一定要包含一个以城市名称命名的标题, 以页面的顶端为中心 。

     Summary
    ::摘要

    • Tree diagrams are a way to organize events and outcomes.
      ::树形图是组织活动和结果的一种方式。
    • Outcomes can be equally likely (the same probability) or not equally likely (different probabilities).
      ::结果可能具有同等可能性(同一概率),也可能不具有同等可能性(不同概率)。
    • If there is more than one event, multiply the outcomes of each to figure of the total number of outcomes.
      ::如果出现不止一个事件,则将每个事件的结果乘以结果总数的数字。