章节大纲

  • 常规

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  • 空间和事件样本

    lesson content

    Jacqueline prepares the Halloween bowl for trick-or-treaters with equal numbers of Reese's, Kit Kat, Twix and M&Ms. Her first trick-or-treater randomly pulls a candy bar from the bowl, puts it back, then randomly pulls another candy bar from the bowl. Jacqueline wonders how many outcomes are possible from the sample space for the two candy bar pulls from the bowl.
    ::Jacqueline 准备万圣节碗, 给和Reese、 Kit Kat、 Twix 和 M&Ms 数量相等的骗子或骗子准备万圣节碗。 她的第一把糖果棒随机地从碗里抽出一个糖果棒,放回去,然后随机地从碗里抽出另一个糖果棒。 Jacqueline 想知道从试样空间中,从碗里抽出两个糖果棒可以产生多少结果。

    In this concept, you will learn about sample spaces.
    ::在这个概念中,你会了解样本空间。

    Sample Spaces
    ::样本空间

    When you conduct an experiment , there are many possible outcomes. If you are doing an experiment with a coin, there are two possible outcomes because there are two sides of the coin. You can either have heads or tails. If you experiment with a number cube, there are six possible outcomes because there are six sides of the number cube and the sides are numbered one to six. We can think of all of these possible outcomes as the sample space .
    ::当您进行实验时, 可能会有许多结果。 如果您正在用硬币做实验, 可能会有两个结果, 因为硬币有两面。 您可以有头或尾。 如果您用数字立方体做实验, 可能会有六个结果, 因为数字立方体有六边, 并且方块是一到六。 我们可以把这些结果都当作样本空间 。

    A sample space is the set of all possible outcomes for a probability experiment or activity. For example, on the spinner there are 5 different colors on which the arrow can land. The sample space, S , for one spin of the spinner is then:
    ::试样空间是概率实验或活动的所有可能结果的一组。 例如, 在旋轴上, 箭头可以降落的颜色有 5 种。 试样空间 S , 对于旋轴的一个旋转是 :

    S = red, yellow, pink, green, blue
    ::红色、黄色、粉红色、绿色、蓝色

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    These are the only outcomes that result from a single spin of the spinner.
    ::这些都是唯一的结果 产生于一个螺旋的一螺旋。

    Changing the spinner changes the sample space. This second spinner still has 5 equal-sized sections. But its sample space now has only 3 outcomes:
    ::改变旋转器改变样本空间。 第二个旋转器仍然有 5 个大小相等的区块。 但现在其样本空间只有 3 个结果 :

    S = red, yellow, blue
    ::红色、黄色、蓝色

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    Let’s look at an example with sample spaces.
    ::让我们看看样本空间的例子。

    A small jar contains 1 white, 1 black, and 1 red marble. If one marble is randomly chosen, how many possible outcomes are there in the sample space?
    ::一个小罐子含有1个白色、1个黑色和1个红色大理石。如果随机选择一个大理石,样本空间中可能有多少结果?

    Since only a single marble is being chosen, the total number of possible outcomes, or sample space matches the marble colors.
    ::由于只选择了单一的大理石,因此可能的结果总数或样本空间与大理石颜色相符。

    S = white, black, red
    ::S=白、黑、红

    Sometimes, the sample space can change if an experiment is performed more than once. If a marble is selected from a jar and then replaced and if the experiment is conducted again, then the sample space can change. The number of outcomes is altered. When this happens, we can use and multiplication to help us figure out the number of outcomes in the sample space.
    ::有时,如果实验不止一次进行,样本空间会改变。如果大理石从罐子里挑选出来,然后替换,如果再次进行实验,则样本空间会改变。结果的数量会改变。当发生这种情况时,我们可以使用和乘法帮助我们找出样本空间中的结果数量。

    A jar contains 1 white and 1 black marble. If one marble is randomly chosen, returned to the jar, then a second marble is chosen, how many possible outcomes are there?
    ::罐中含有1个白色大理石和1个黑色大理石。如果随机选择一个大理石,返回罐中,则选择第二个大理石,结果有多少?

    This is a situation where a tree diagram is very useful. Consider the marbles one at a time. After the first marble is chosen, it is returned to the jar so now there are again two choices for the second marble.
    ::这是树图非常有用的情况。 一次考虑大理石。 在选择了第一个大理石后, 将大理石还给罐子, 所以现在第二大理石又有两个选择。

    Use a tree diagram to list the outcomes.
    ::使用树形图来列出结果。

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    From the tree diagram, you can see that the sample space is:
    ::从树图中,你可以看到样本空间是:

    S = white-white, white-black, black-white, black-black
    ::S=白白 白黑 黑黑 黑白 黑黑

    We could also multiply by multiplying the two options and the number of selections.  Two marble colors and two selections:
    ::我们也可以乘以两种选择和选择的数量。

    2 × 2 = 4

    There are four outcomes in the sample space.
    ::样本空间有四个结果。

    Examples
    ::实例

    Example 1
    ::例1

    Earlier, you were given a problem about Jacqueline and her curiosity about the candy from the Halloween bowl.
    ::早些时候,你得到一个问题 关于杰奎琳 和她好奇 从万圣节碗的糖果。

    The trick-or-treater pulled one time randomly, returned the candy bar to the bowl, then pulled randomly once more.  How many possible outcomes are there from the two pulls?
    ::诡计或捣蛋者曾随机拉了一次,把糖果棒还给碗里,然后又随机拉一次。两次拉了多少结果?

    First, list the different candy choices:
    ::首先列出不同的糖果选择:

    Twix, Reese's, M&Ms, Kit Kat
    ::Twix, Reese's, M & MM, Kit Kat Kat , Twix, Reese's, MM & MM, Kit Kat 和 Kit Kat 和 Kit Kit 和 Kit 和 Kit 和 Kit 和 Kit 和 Kit 和 Kit 和 Kit 和 Kit 和 Kit 和 Kit 和 Kit 和 Kit 和 Kit 和 Kit 和 Kit 和 Kit 和 Kit 和 Kit 和 Kit Kit 和 Kit 和 Kit 和 Kit 和 Kit 和 Kit 和 Kit 和 Kit 和 Kit 和 K K K 和 K 和 K K K 和 K K K K K 和 K K K K K K K K K K K K K K 和 K K K K K K 和 K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K 的 K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K

    Next, list the possible outcomes of Pull 1 and Pull 2:
    ::下一份,列出 " 1号 " 和 " 2号 " 的可能结果:

    Pull 1:                  Twix                                                      M&Ms                        
    ::第1拉拉:Twix MM & MM & MM

    Pull 2:   Twix   Reese's  M&Ms     Kit Kat            Twix  Reese's  M&Ms  Kit Kat 
    ::Pull2:Twix Reese的MM & MM Kit Kat Twix Reese的MM & MM Kit Kat Twix Reese的MM & MM Kit Kat

    Pull 1:                 Reese's                                                  Kit Kat
    ::拉1: 里瑟的外衣

    Pull 2:   Twix  Reese's   M&Ms    Kit Kat            Twix  Reese's   M&Ms   Kit Kat
    ::Pull2:Twix Reese的MM & MM Kit Kat Twix Reese的MM & MM Kit Kat Twix Reese的MM & MM Kit Kat

    Then, list the sample space, or all possible outcomes of the two pulls from the candy bowl:
    ::然后,列出样本空间,或者从糖果碗中拉出两只手的所有可能结果:

    Twix-Twix, Twix-Reese's, Twix-M&Ms, Twix-Kit Kat, M&Ms-Twix, M&Ms-Reese's, M&Ms-M&Ms, M&Ms-Kit Kat, Reese's-Twix, Reese's-Reese's, Reese's-M&Ms, Reese's-Kit Kat, Kit Kat-Twix, Kit Kat-Reese's, Kit Kat-M&Ms, Kit Kat-Kit Kat
    ::Tix-Twix-Twix-Reese、Twix-Reese、Twix-M&Ms、Twix-Kit Kat、M&Ms-Twix、M&M-Ms-MTM、M&M-Kit Kat、Reese的Twix、Reese的Reseseses、Reese的M&M、Reese的Kit的Kit Kit、Kit Kat-Twix、Kit Kate Kat-Reesese的M&Ms、Kit Kat-M&Ms、Kit Kat-Kit Kit Kat Kit

    The answer is there are 16 possible outcomes.
    ::答案是,有16个可能的结果。

    Example 2
    ::例2

    June flipped a coin three times. How many outcomes are in the sample space?
    ::June翻了硬币三次 样本空间有多少结果?

    First, make a list of the possible outcomes for each flip.
    ::首先,列出每个翻转的可能结果列表。

    Heads
    ::主管 主管 主管 主管 主管

    Tails
    ::反反面

    Next, count the number of the possible outcomes for each flip.
    ::接下来,计算每个翻转的可能结果数 。

    There are two outcomes for each flip of a coin: heads or tails.
    ::硬币的每翻一个硬币就有两个结果:头或尾。

    Then, multiply the number of outcomes by the number of flips.
    ::然后,将结果数乘以翻转数。

    June flipped the coin three times.
    ::June把硬币翻了三次

    2 × 3 = 6

    The answer is there are 6 outcomes in the sample space.
    ::答案是样本空间有6个结果。

    Example 3
    ::例3

    How many outcomes are in the sample space of three spins of a spinner with red, blue, yellow and green?
    ::红色、蓝色、黄色和绿色的脊柱的三个旋转空间的样本空间中有多少结果?

    First, make a list of the possible outcomes for each spin.
    ::首先,列出每个旋转的可能结果清单。

    Red
    ::红红

    Blue
    ::蓝蓝色

    Yellow 
    ::黄黄黄色

    Green
    ::绿绿色

    Next, count the number of possible outcomes for each spin.
    ::接下来,计算每个旋转时可能取得的结果的数量。

    There are four possible outcomes for each spin:  red, blue, yellow, green.
    ::每个旋转都有四种可能的结果:红色、蓝色、黄色、绿色。

    Then, multiply the number of outcomes by the number of spins.
    ::然后,将结果数乘以旋转数。

    June flipped the coin three times.
    ::June把硬币翻了三次

    4 × 3 = 12

    The answer is there are 12 outcomes in the sample space.
    ::答案是样本空间有12个结果。

    Example 4
    ::例4

    What is the sample space for the roll of a number cube numbered 1–6 and how many possible outcomes are there from one roll?
    ::编号 1 - 6 的数立方体滚动的样本空间是多少? 从一个滚动中可以得出多少结果?

    First, determine all possible outcomes:
    ::首先,确定所有可能的结果:

    1, 2, 3, 4, 5, 6

    Next, count the number of possible outcomes for one roll:
    ::下一步,计算一个卷的可能结果数:

    There are 6 possible outcomes:  1, 2, 3, 4, 5, 6
    ::可能的成果有6个:1、2、3、4、5、6

    Then, multiply the number of outcomes by the number of rolls.
    ::然后,将结果数乘以滚动数。

    Since we are only rolling once, the number of possible outcomes is 6. 
    ::由于我们只滚动过一次,可能的结果是6个。

    The answer is the sample space is 1, 2, 3, 4, 5, 6 and the number of possible outcomes is 6.
    ::答案是样本空间是 1, 2, 3, 4, 4, 5, 6, 可能的结果是 6。

    Example 5
    ::例5

    A bag with a blue and a red marble. One marble is drawn and then replaced. What is the sample space?
    ::装有蓝色和红色大理石的大理石的袋子,一个大理石被绘制,然后被替换。

    First, list the possible outcomes for each draw:
    ::首先,列出每一提款的可能结果:

    blue
    ::蓝蓝色

    red
    ::红色红

    Next, list the possible outcomes for Draw 1 and Draw 2:
    ::下一步,列出第1版和第2版的可能结果:

    Draw 1:                    red                     blue
    ::绘制1:红色蓝色

    Draw 2:              red    blue             red     blue
    ::绘制 2: 红色蓝色 红色 蓝色 蓝色 红色 蓝色

    Then, list all possible outcomes from the two draws:
    ::然后列出这两条提法的所有可能结果:

    red-red, red-blue, blue-red, blue-blue
    ::红色 红色 蓝色 蓝色 蓝色 蓝色 蓝色 蓝色 蓝色

    The answer is the sample space is red-red, red-blue, blue-red, blue-blue
    ::答案是 样本空间是红色 红色 蓝色 蓝色 蓝色 蓝色 蓝色

    Review
    ::回顾

    Answer the following questions about sample spaces.
    ::回答下列关于抽样空间的问题。

    1. What is the size of the sample space for a single toss of a number cube?
      ::数字立方体的单次平方体的试样空间大小是多少 ?
    2. What is the size of the sample space for a single flip of a coin?
      ::一枚硬币的试样空间大小是多少?
    3. A coin is flipped two times. List all possible outcomes for the two flips.
      ::一个硬币被翻了两次。 列出两个硬币的所有可能结果 。
    4. A coin is flipped three times in a row. List all possible outcomes for the two flips.
      ::硬币一行翻三次。 列出两个硬币的所有可能结果 。
    5. A bag contains 3 ping pong balls: 1 red, 1 blue, and 1 green. What is the sample space for drawing a single ball from the bag?
      ::包里装有3个乒乓球:1个红球、1个蓝色球和1个绿色球。从包里抽出单球的样本空间是多少?
    6. A bag contains 3 ping pong balls: 1 red, 1 blue, and 1 green. What is the sample space for drawing a single ball, returning the ball to the bag, then drawing a second ball?
      ::包装有3个乒乓球:1个红球、1个蓝色球和1个绿色球。画一个单球、把球还给袋子、然后画第二个球的样本空间是什么?
    7. What is the sample space for a single spin of the with red, blue, yellow and green sections spinner?
      ::用红色、蓝色、黄色和绿色部分脊柱旋转的单旋转的样本空间是什么?
    8. What is the sample space for 2 spins of the first spinner?
      ::第一个旋转器的 2 个旋转的样本空间是什么 ?
    9. What is the sample space for three spins of the spinner?
      ::旋转器三个旋轴的样本空间是什么?
    10. A box contains 3 socks: 1 black, 1 white, and 1 brown. What is the sample space for drawing a single sock, NOT returning the sock to the box, then drawing a second sock?
      ::框中包含3只袜子:1只黑袜子,1只白袜子,1只棕袜子。绘制单袜子的样本空间是多少,不将袜子还回盒子,然后绘制第二只袜子?
    11. A box contains 3 socks: 1 black, 1 white, and 1 brown. What is the sample space for drawing all 3 socks from the box, one at a time, without returning any of the socks to the box?
      ::盒子里有3只袜子:1只黑袜子,1只白袜子,1只棕袜子。从盒子里抽出全部3只袜子的样本空间是多少,一次一个,不把任何袜子还回盒子里?
    12. True or false. A sample space is the total possible outcomes.
      ::试样空间是全部可能的结果。
    13. True or false. A sample space is a percentage.
      ::不管是真实的还是虚假的 样本空间是百分比

    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 。