12.17树形图

章节大纲

• 选择节常规

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• 选择节树形图

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  树形图

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  [Figure 1]

  
  ::[图1]

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  After running out of the haunted house, Sheila and her friends stopped a few minutes to catch their breath. Then they each gave the door attendant another ticket and ran back inside. After 10 minutes, they exited running and screaming. When they walked back up to the entrance, Charles, who was taking tickets at the door, asked them how many tickets had they used going in the haunted house. Sheila turned and asked Tonja and Annette how many times they went in together without her. They told her they had been in 2 times before she got there. How can Sheila figure out how many tickets they have used on admission to the haunted house?
  ::Sheila和她的朋友们跑出闹鬼屋后几分钟停下来喘口气,然后每人给门服务员一张门票,然后跑回屋里,10分钟后,他们就跑出来尖叫。当他们走到入口处时,Charles在门前领取门票,问他们用多少张门票进入闹鬼屋。Sheila转过身,问Tonja和Annette有多少张门票没有带她一起进去,他们告诉她,在她到那里之前,他们已经去过两次了。Sheila如何知道他们用多少张门票进入闹鬼屋?

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  In this concept, you will learn to use the   and tree diagrams to calculate  outcomes .
  ::在此概念中,您将学会使用树图和树图来计算结果。

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  Using Tree Diagrams to Calculate Outcomes
  ::使用树图图来计算结果

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  When thinking about  probability , you think about the chances or the likelihood that an  event  is going to occur. Calculating probability through a ratio is one way of looking at probability. You can also think about chances or probability by calculating  outcomes . An  outcome  is an end result. When you have multiple options you can calculate an outcome or figure out how many possible outcomes there are.
  ::思考概率时, 您会考虑事件发生的概率或概率。 通过比率计算概率是观察概率的一种方式。 您也可以通过计算结果来思考概率或概率。 结果是最终结果。 当您有多个选项时, 您可以计算结果或找出有多少可能的结果 。

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  There are a couple of different ways to figure outcomes, including constructing a  tree diagram , which is a visual way of listing outcomes.
  ::有几种不同的方式来描述结果,包括绘制树图,这是列出结果的直观方式。

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  Let’s construct a tree diagram.
  ::让我们建树图吧。

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  Jessica has four different favorite types of ice cream. She loves vanilla crunch, black raspberry, chocolate chip, and lemonade. She also loves two different types of cones, a plain cone and a sugar cone. Given these flavors and cones choices, how many different single scoop ice cream cones can Jessica create?
  ::杰西卡有四种不同的冰淇淋。她喜欢香草冰淇淋、黑莓、巧克力芯片和柠檬汁。她也喜欢两种不同的锥子,一种普通锥子和甘蔗。根据这些口味和锥子的选择,杰西卡能创造多少不同的冰淇淋锥?

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  To solve this problem, you are going to create a tree diagram.
  ::为了解决这个问题,你将创建一个树图。

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  First, list the choices of ice cream.
  ::首先,列出冰淇淋的选择。

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  Vanilla Crunch
  ::香草香草库

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  Black Raspberry
  ::黑草莓

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  Chocolate Chip
  ::巧克力芯片

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  Lemonade
  ::柠檬

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  Next, add in the two cone types. Each flavor has two possible cone types that it could go on. This is where the tree diagram part comes in.
  ::接下来,添加两种锥形。每种口味都有两种锥形,可以继续。这是树图部分进入的地方。

  

  [Figure 2]

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  Here you have four different flavors, and two types of cones, which mean you have 8 possible ice cream cone options.
  ::这里有四种不同的口味, 两种锥子, 这意味着你有8种可能的冰淇淋甜筒选择。

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  You can see that the number of choices multiplied by the number of variables gave us the total number of outcomes.
  ::您可以看到,选择的数量乘以变量的数量 给了我们结果的总数。

  $\begin{array}{r}4\times 2=8\end{array}$

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  This is called the  Fundamental Counting Principle (FCP)  and it can be very useful if you don’t want to draw an elaborate diagram to figure out your options.
  ::这叫做基本计数原则(FCP), 如果您不想绘制一个详细的图表,

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  Examples
  ::实例

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  Example 1
  ::例1

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  Earlier, you were given a problem about Cheryl, Tonja, and Annette at the haunted house.
  ::早些时候,你得到一个问题 关于Cheryl, Tonja, 和安妮特 在闹鬼的房子。

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  After catching up with her friends, Tonja and Annette, at the haunted house, Sheila and her friends spent one ticket each time they went in the haunted house. Tonja and Annette went in the haunted house two times before Sheila got there. The three of them went in twice together. Sheila wants to how many tickets the three of them have spent going in the haunted house.
  ::Sheila和她的朋友每次进闹鬼屋时都花一张票。 Tonja和Annette在Sheila到那里之前两次进闹鬼屋。他们中的三人一起进两次。Sheila想了解他们中的三人在闹鬼屋里花过多少票。

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  How can Sheila figure out how many tickets the three of them have used at the haunted house?
  ::Sheila怎么知道他们三人在鬼屋里 用了几张票?

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  Sheila can draw a tree diagram or use the Fundamental Counting Principle to solve this problem.
  ::Sheila可以绘制树图或使用基本计数原则解决这个问题。

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  First, using the Fundamental Counting Principle, Sheila needs to divide the problem into two.
  ::首先,根据基本计数原则,希拉需要将问题分为两个。

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  How many tickets did Tonja and Annette use together before she came?
  ::Tonya和Annette来之前 一起用过几张票?

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  $\begin{array}{r}C(2,2)\end{array}$
  ::C (2 , 2 )

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  How many tickets did Sheila, Tonja, and Annette use together?
  ::希拉、托尼娅和安妮特一起用过几张票?

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  $\begin{array}{r}C(2,3)\end{array}$
  ::C(2 , 3 )

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  Next, figure out the possible number of combinations by multiplying.
  ::接下来,通过乘法找出组合的可能数量。

  $$\begin{array}{r}\begin{array}{r}2\times 2=4\\ 2\times 3=6\end{array}\end{array}$$

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  Then, add the two results.
  ::然后加上两个结果。

  $\begin{array}{r}4+6=10\end{array}$

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  The answer is the three of them spent 10 tickets going in the haunted house.
  ::答案是他们三人花了10张门票 进鬼屋

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  Example 2
  ::例2

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  Evaluate  $\begin{array}{r}C(9,4)\end{array}$ .
  ::评价C(9,4)

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  To figure out the possible number of combinations, simply multiply.
  ::要找出可能的组合数, 简单的乘法 。

  $\begin{array}{r}9\times 4=36\end{array}$

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  The answer is 36.
  ::答案是36岁

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  Find the outcomes in the following examples. You may draw a tree diagram or use the Fundamental Counting Principle (FCP) to answer each questio n.
  ::在以下示例中查找结果。您可以绘制树形图或使用基本计数原则(FCP)回答每个问题。

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  Example 3
  ::例3

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  Sarah has three pairs of pants and four shirts. How many different outfits can she create with these choices?
  ::Sarah有三条裤子和四件衬衫 她能用这些选择创造多少不同的衣服?

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  First, multiply the number of choices by the number of variables to get the total number of outcomes.
  ::首先,将选择数乘以变量数,得出结果总数。

  $\begin{array}{r}3\times 4=12\end{array}$

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  The answer is 12 outfits.
  ::答案是12套衣服

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  Example 4
  ::例4

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  Travis has four different pairs of striped socks and two pairs of sneakers, one red and one blue. How many different shoe/sock combinations can Travis create?
  ::Travis有四双不同的条纹袜子和两双运动鞋,一双红色,一双蓝色。Travis能创造多少不同的鞋/袜子组合?

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  First, multiply the number of choices (4 pairs of socks) by the number of variables (2 pairs of sneakers) to get the total number of outcomes.
  ::首先,将选择数(4对袜子)乘以变量数(2对运动鞋),得出结果总数。

  $\begin{array}{r}4\times 2=8\end{array}$

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  The answer is 8 combinations.
  ::答案是8个组合

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  Example 5
  ::例5

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  If there are 33 ice cream flavors and two types of cones, how many different single scoop ice cream cones can you create?
  ::如果有33种冰淇淋口味和两种锥子, 你能够创造多少种不同的冰淇淋锥?

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  First, multiply the number of choices (33 flavors) by the number of variables (2 cones) to get the total number of outcomes.
  ::首先,将选择数(33口味)乘以变量数(2锥体),得出结果总数。

  $\begin{array}{r}33\times 2=66\end{array}$

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  The answer is 66 combinations.
  
  ::答案是66个组合

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  Review
  ::回顾

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  Design a tree diagram or use the Fundamental Counting Principle to determine each set of outcomes.
  ::设计一棵树图或使用基本计数原则来确定每组结果。

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  1. Jessica has three skirts and four sweaters. How many possible outfits can she arrange given her clothing?
     ::杰西卡有三条裙子和四件毛衣 她能安排多少衣服?
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  2. Kim loves ice cream. She has the option of vanilla, chocolate or strawberry ice cream and she has different toppings to put on her ice cream cone. If she has sprinkles, hot fudge and nuts to choose from, how many different ice cream cones can she create with those toppings?
     ::金爱吃冰淇淋。她有香草、巧克力或草莓冰淇淋的选择,她有不同的奶油加冰淇淋甜筒。 如果她有洒水、热软糖和坚果可以选择,她能用这些奶油甜筒创造多少不同的冰淇淋甜筒?
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  3. There are five possible surfboard designs and two possible colors. How many possible surfboards can be created from these options?
     ::有五种可能的冲浪板设计和两种可能的颜色。 从这些选项中可以创建多少个可能的冲浪板?
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  4. Team sweatshirts come in four colors and three sizes. How many sweatshirt outcomes are possible?
     ::团队运动衫有四种颜色和三种尺寸。 有多少运动衫可以产生结果?
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  5. A diner offers six types of toast with either scrambled or fried eggs. How many breakfast options are there?
     ::一家餐厅提供六种面包 要么炒鸡蛋 要么炒鸡蛋
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  6. The same diner is offering a special that adds orange or apple juice with the eggs and toast. How many different breakfast options are there now?
     ::同一家餐厅正在提供一份特别菜,配上橙汁或苹果汁,配上鸡蛋和烤面包。现在有多少不同的早餐选择?
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  7. If the diner adds in coffee as a beverage choice with the other options, how many different breakfast options can you have now?
     ::如果餐厅加上咖啡作为饮料选择, 加上其他选择, 你现在有多少不同的早餐选择?
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  8. If the diner also adds in a choice of bacon or sausage, how many different breakfast options do you have now?
     ::如果餐厅也增加培根或香肠的选择, 你现在有多少不同的早餐选择?
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  9. An Italian restaurant offers penne pasta, shells or spaghetti with a choice of vegetable, meat or plain sauce. How many different pasta dishes are possible given these options?
     ::意大利餐厅提供食用面食、贝壳或意大利面,可选择蔬菜、肉类或平质酱。
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  10. If they also offer a choice of Italian bread or garlic bread, how many options are possible?
      ::如果它们也选择意大利面包或大蒜面包,可以选择多少种选择?
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  11. If they add in the choice of a Caesar salad or a tossed salad, how many meal options are there now?
      ::如果他们在选择凯撒沙拉或乱扔沙拉时 增加多少餐具?
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  12. If they offer a choice of ice cream or cheesecake with the meal, how many meal options are there now?
      ::如果他们选择吃冰淇淋或芝士蛋糕, 现在有多少餐具?
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  13. For a new tennis racquet, Danny can choose from 8 different brands, 3 different head sizes, and 4 different grip sizes. How many different racquet choices does Danny have?
      ::对于新的网球场来说,Danny可以选择8个不同的品牌,3个不同的头大小,4个不同的控制大小。 Danny可以选择多少个不同的球场?

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  Review (Answers) 
  ::回顾(答复)

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  Click   to see the answer key or go to the Table of Contents and click on the Answer Key under the 'Other Versions' option.
  ::单击可查看答题键, 或转到目录中, 单击“ 其他版本” 选项下的答题键 。

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  Resources
  ::资源