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  • 使用树图

    lesson content

    Luis is making a sandwich and has a number of different ingredients available. He can choose between white bread and wheat bread, swiss cheese and cheddar cheese, and for meat he can choose turkey, ham or tuna. Based on these variables, how many different kinds of sandwiches can Luis make?
    ::路易斯正在做一个三明治,并且有多种不同的成分。他可以在白面包和小麦面包、三明治奶酪和切达干酪之间做出选择,对于肉类,他可以选择火鸡、火腿或金枪鱼。 根据这些变量,路易斯可以做多少种不同的三明治?

    In this concept, you will learn to calculate probability by using tree diagrams.
    ::在此概念中,您将学习使用树形图计算概率。

    Tree Diagram
    ::树图图

    Probability is a mathematical way of calculating how likely an event is likely to occur. An event is a result of an experiment or activity that might include such things as:
    ::概率是一种计算事件发生可能性的数学方法。一个事件是实验或活动的结果,其中可能包括:

    • flipping a coin
      ::翻硬币
    • spinning a spinner
      ::旋转旋转旋转器
    • rolling a number cube
      ::滚动数字立方体
    • choosing an item from a jar or bag
      ::从罐或袋中选择项目

    An important concept when calculating probability is to think about outcomes . An outcome is a possible result of some event occurring. When you flip a coin, “heads” is one outcome; tails is a second outcome. Total outcomes are computed simply by counting all possible outcomes.
    ::计算概率时的一个重要概念是思考结果。结果是某些事件的可能结果。当您翻硬币时,“头”是一个结果;尾是第二个结果。总结果仅通过计算所有可能的结果来计算。

    One good way to count the total number of outcomes for an event is to make a tree diagram . A tree diagram is a branching diagram that shows all possible outcomes for an event.
    ::计算事件结果总数的一个好方法就是绘制树图。树图是一个分支图,显示事件的所有可能结果。

    Let’s look at an example.
    ::让我们举个例子。

    If you flip a coin two times, how many different outcomes are possible?
    ::如果你翻硬币两次, 有多少不同的结果是可能的?

    First, make a tree diagram. To make a tree diagram, split the different events into either-or choices. The first choice breaks flip 1 down into heads or tails. Each outcome of flip 1 is broken down again for flip 2.
    ::首先,绘制一棵树图。要绘制一棵树图,将不同的事件分成一个或两个或几个选择。第一个选择将1个事件分为头或尾。翻1个事件的结果将再次细分为翻2个。

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    Next, analyze the tree diagram. The pink box shows the total number of outcomes for both flips:
    ::接下来分析树图。粉红色框显示两个翻转的结果总数 :

    heads - heads
    ::- 头 - 头 - 头

    heads - tails
    ::- 头尾

    tails - heads
    ::尾尾尾 - 头

    tails - tails
    ::尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾尾

    The answer is 4.
    ::答案是4。

    There are 4 possible outcomes.
    ::有4种可能的结果。

    What happens when you increase the number of flips to three? Just add another section to your tree diagram.
    ::当你把翻转数增加到三个时会怎样?

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    In all, there are now 8 total outcomes.
    ::总而言之,现在共有8项总成果。

    H H H T T T H H T T T H H T H T H T H T T T H H

    ::希图图图图图图图图图图图图图图图图图图图图图图图图图图图图图图图图图图图图图图图图图图图图图图图图图图图图图图图图图图图图图

    Examples
    ::实例

    Example 1
    ::例1

    Earlier, you were given a problem about Luis and his sandwiches. He needs to figure out how many sandwiches he could make.
    ::他需要弄清楚他能做多少三明治

    First, to figure this out, Luis can create a tree diagram to show all of his choices and calculate the sandwich outcomes.
    ::首先,为了弄清楚这一点,路易斯可以创建一个树图, 显示他的所有选择, 计算三明治结果。

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    Next, Luis will count up the number of options of sandwich choices.
    ::接下来,路易斯将计算三明治选择的选项数。

    You can see that the tree diagram begins with the bread choices, then adds the second layer of the cheese options, and finally adds the meat choices. Therefore there are 12 possible options.
    ::您可以看到树图以面包选择开头, 然后添加奶酪选择的第二层, 最后添加肉类选择。 因此有12种可能的选择。

    The answer is 12.
    ::答案是12岁

    There are twelve possible sandwich outcomes for Luis.
    ::Luis有12种可能的三明治结果。

    Example 2
    ::例2

    How many possibilities are there for a win-win-win?
    ::双赢有多少可能性?

    List the possible outcomes for the three games.
    ::列出这三场比赛的可能结果 。

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    You can see that when you break out all of the options (the pink column) that there is one chance for a win-win-win.
    ::当你打破所有选项(粉红色柱)时,你可以看到,有一个双赢的机会。

    Example 3
    ::例3

    A car has four seats. How many different options are there if three people ride in the car? Use a tree diagram to calculate the total possible outcomes.
    ::一辆汽车有四个座位。 如果三个人坐进汽车, 有多少不同的选择? 使用树图来计算可能的总结果 。

    First, draw the tree diagram.
    ::首先,绘制树图。

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    Next, count the number of possible outcomes (in orange).
    ::其次,计算可能的结果的数量(橙色)。

    There are 12 orange squares.
    ::有12个橙色方形

    The answer is 12.
    ::答案是12岁

    The answer is that there are 12 options.
    ::答案是,有12种选择。

    Example 4
    ::例4

    Candice has two skirts, three shirts and two different sweaters. How many possible outfits can she create? Use a tree diagram to calculate the total possible outcomes.
    ::Candice有两条裙子、三件衬衫和两件不同的毛衣。 她能制造多少件可能的衣服? 使用树图来计算可能的总结果 。

    First, draw the tree diagram.
    ::首先,绘制树图。

    lesson content

    Next, count the number of possible outcomes (in blue).
    ::其次,计算可能的结果数目(蓝色)。

    There are 12 blue squares.
    ::有12个蓝方。

    The answer is 12.
    ::答案是12岁

    The answer is that there are 12 options.
    ::答案是,有12种选择。

    Example 5
    ::例5

    Sam is trying to create a pizza. He has two crust options, four different cheese options and 8 different toppings to choose from. How many pizzas can he make if he only chooses one topping? Use a tree diagram to calculate the total possible outcomes.
    ::Sam试图创建比萨饼。 他有两个地壳选择, 四个不同的奶酪选择, 还有八个不同的图。 他只能选择一个披萨, 可以做多少披萨? 使用树图来计算可能的总结果 。

    First, draw a tree diagram. Because of the number of choices, you can draw the tree diagram for one crust choice and double your options for the second crust type.
    ::首先,绘制一棵树图。根据选择的数量,您可以绘制一个地壳选择的树图,并将第二个地壳类型的选择增加一倍。

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    Next, count the total options for the first crust choice.
    ::接下来,计算第一个地壳选择的总选项 。

    There are 32 possible choices of one cheese and one topping for one crust choice.
    ::一种奶酪有32种可能的选择,一种是地壳选择,一种是奶油。

    Then, double your options since you have two choices of crust. 
    ::然后,加倍你的选择 因为你有两种选择的地壳。

    32 × 2 = 64

    The answer is 64.
    ::答案是64。

    Therefore Sam has 64 different options for his pizza with one topping.
    ::所以Sam有64种不同的比萨饼 配一个托普

    Review
    ::回顾

    Use a tree diagram to figure out all of the different outcomes.
    ::使用树图来解析所有不同的结果 。

    1. Jeff’s Jet Ski rentals have 3 different Jet Ski models: the single, the double, and the racer. Renters can rent for a half hour or a full hour. How many rental choices are there?
    ::1. 杰夫的喷气滑翔机租赁有三种不同的喷气滑翔机模型:单型、双型和赛车手。 租房者可以租一个半小时或一个小时。 有多少租房选择?

    2. Cable Com offers Basic Cable, Premium Cable, and Super Premium Cable service. Cable Com offers these services for home use, small business use, or large business use. How many different cable choices are there?
    ::2. 有线电视公司提供基本电缆、有价证券和超级有价证券服务;有线电视公司为家庭使用、小企业使用或大型商业使用提供这些服务。

    3. The Gotham Gazette offers the following newspaper choices:
    ::3. 《哥谭公报》提供以下报纸选择:

    • home or office delivery
      ::家庭或办公室交付或办公室交付
    • weekdays only, weekends only, or all seven day delivery
      ::仅工作日、仅周末或所有七天分娩
    • monthly or weekly payments
      ::每月或每周支付

    How many different kinds of choices can you get?
    ::你能得到多少种不同的选择?

    4. On Main Street, Jiri has to go through 4 traffic lights that can be either red or green. How many different outcomes are there for the 4 lights?
    ::4. 在主街,吉日必须通过4个红灯或绿灯,4个灯有多少不同结果?

    5. I-Cone high tech ice cream shop offers the following options.
    ::5. I-Cone高科技冰淇淋店提供以下选择。

    • cone: sugar, waffle
      ::甜甜、华夫饼
    • size: teeny, mega, huge
      ::大小: 青少年, 巨型, 巨型
    • flavors: shocking blueberry, marvelous mango, chocolate attack
      ::味道: 惊人的蓝莓 奇妙的芒果 巧克力袭击

    How many different choices are there?
    ::有多少不同的选择?

    6. To remodel her kitchen, Gretchen has the following choices: Floor: tile or wood; Counter: Granite or Formica; Sink: white, steel, stone. How many different choices can Gretchen make?
    ::6. 为了改造厨房,格雷琴有以下选择:地板:瓷砖或木头;反面:格拉尼特或福米卡;辛克:白色、钢、石。格雷琴可以作出多少不同的选择?

    7. Jeff has five different pairs of socks and three pairs of shoes. How many possible combinations are there?
    ::7. Jeff有五双不同的袜子和三双鞋子,有多少可能的组合?

    8. What if Jeff has six different pairs of socks and three pairs of shoes? How many possible combinations are there?
    ::8. 如果杰夫有六双不同的袜子和三双鞋子呢?

    9. What if Jeff has six different pairs of socks and four pairs of shoes? How many possible combinations are there?
    ::9. 如果杰夫有六双不同的袜子和四双鞋子呢?

    10. What if Jeff has eight different pairs of socks and three pairs of shoes? How many possible combinations are there?
    ::10. 如果杰夫有八双不同的袜子和三双鞋子呢?

    11. Jessie has three sweaters, two turtlenecks and three jackets. How many possible combinations are there?
    ::11. 杰西有三件毛衣,两件高领和三件外套。

    12. What if Jessie has two sweaters, three turtlenecks and three jackets? How many possible combinations are there?
    ::如果杰西有两件毛衣,三件高领和三件夹克呢?

    13. What if Jessie has four sweaters, three turtlenecks and three jackets? How many possible combinations are there?
    ::13. 如果杰西有四件毛衣,三件高领衣和三件夹克呢?

    14. What if Jessie has three sweaters, two turtlenecks, two scarfs and three jackets? How many possible combinations are there?
    ::14. 如果杰西有三件毛衣,两件头领,两条围巾和三件夹克呢?

    15. What if Jessie has four sweaters, two turtlenecks, two scarfs and three jackets? How many possible combinations are there?
    ::如果杰西有四件毛衣,两件头领,两条围巾和三件夹克呢?

    Review (Answers)
    ::回顾(答复)

    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 。

     

    Resources
    ::资源