12.15概率的测量

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  概率的测量

  

  [Figure 1]

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  Becky and her friends entered a drawing at a local store for a trip to an amusement park. Only the first 50 people to enter the store were allowed to participate in the drawing. Becky, Kaye, and Amy each entered their name in the drawing. How can Becky use the information to write a statement of  probability  about her chances of winning then express it as a fraction, decimal, and percent?
  ::贝基和她的朋友在当地一家商店里登上了一张图,前往游乐场旅行。 只有头50名进入该店的人获准参与绘画。 贝基、凯伊和艾米每人在绘画中都输入了自己的名字。 贝基如何利用这些信息写出关于她胜出概率的说明,然后以小数、小数和百分比表示呢?

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  In this concept, you will learn to describe the probability of events as fractions, decimals or percents.
  ::在此概念中,您将学会将事件概率描述为分数、小数或百分比。

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  Describing Probability
  ::描述概率

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  Fractions  mean a part of a whole. Decimals and percents also mean a part of a whole. Therefore, probabilities can be written as fractions, decimals, or as percents.
  ::分数是指整体的一部分。十进制和百分数也意味着整体的一部分。因此,概率可以以分数、十进制或百分数来表示。

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  Let’s practice writing the following probabilities three different ways.
  ::让我们用三种不同的方式来写下以下概率。

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  Here is a scenario.
  ::情况是这样的。

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  A bag has four cubes in it, a red cube, two yellow cubes and one blue cube. What is the probability of drawing a red or yellow cube out of the bag?
  ::一个袋子里有四个立方体,一个红色立方体,两个黄色立方体和一个蓝色立方体。从袋子里画出一个红色或黄色立方体的概率是多少?

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  First, write a fraction to show the ratio of possible  outcomes  and favorable outcomes. There are four cubes in the bag, so there are four possible outcomes. This is the denominator.
  ::首先, 写一个分数来显示可能的结果和有利结果的比例。 包里有四个立方体, 所以有四个结果。 这是分母 。

  $$\begin{array}{r}\begin{array}{rcl}P& =& \frac{\mathrm{\#}\text{ of favorable outcomes}}{\mathrm{\#}\text{ of possible outcomes}}\\ P& =& \frac{D}{4}\end{array}\end{array}$$

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  Next, determine the favorable outcomes by counting the red and yellow cubes. There are two yellow cubes and one red cube. That means that there are three favorable outcomes.
  ::接下来,通过计算红色和黄色立方体来决定有利结果。有两个黄色立方体和一个红色立方体。这意味着有三个有利结果。

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  $\begin{array}{r}P=\frac{3}{4}\end{array}$
  ::P=3 4 P=3 4

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  This is the answer as a fraction.
  ::这是作为分数的答案 。

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  To convert the fraction to a decimal, find an equivalent fraction with a denominator that is a multiple of 10. In this case, the denominator will be 100. Because you have to multiply 4 by 25 to get a denominator of 100, you have to multiply the numerator by 25.
  ::要将分数转换为小数点,请找到一个等值分数,分母为10的倍数。 在这种情况下,分母将为100。 因为要将分母乘以4乘以25才能得到100的分母, 分子乘以25, 分子必须乘以25。

  $$\begin{array}{r}\begin{array}{rcl}P=\frac{3}{4}& =& \frac{D}{100}\\ 4\times 25& =& 100\\ 3\times 25& =& 75\\ P& =& \frac{75}{100}\text{ or }.75\end{array}\end{array}$$

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  Now, take the decimal and make it a percentage. If you look at the fraction out of 100 it is already clear what the percentage is. The percentage is 75% because percent means out of 100.
  ::现在, 以小数点为小数点, 把它做成一个百分比。 如果您看一看百分数中的分数, 百分比已经很清楚。 百分比是75%, 因为百分数等于100。

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  If you were working with the decimal only, then you move the decimal point two places to the right and then add the % sign. You move it two places because that is hundredths and % means out of 100.
  ::如果仅使用小数点,则将小数点两点移到右侧,然后将% 符号添加到右侧。移动两点是因为百分百和百分率等于100。

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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 Becky and her hope of winning tickets to the amusement park.
  ::早些时候,你得到一个问题 贝琪和她希望赢得 游乐园的门票。

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  Becky read the back of the entry and learned that the winner of the drawing gets to take two friends with them to the amusement park. She’s exhales, relieved that she has a better chance of going to the amusement park because she and her two friends entered the drawing. That makes her have 3 chances instead of 1. To see how good her chances are, she decides to find the probability as a ratio, fraction, and a decimal.
  ::贝基读了条目的背面,并了解到绘画的获胜者可以带两个朋友去游乐园。 她的呼气令她松了一口气,因为她和她的两个朋友进入了游乐园,所以她有更好的机会去游乐园。 这使得她有3个机会,而不是1个机会。 为了看她的机会有多好,她决定找到一个比率、分数和小数的概率。

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  First, write it as a ratio.
  ::首先,把它写成一个比例。

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  There are 50 entries in the drawing, so there are 50 possible outcomes. The denominator is 50. Becky gets to go to the amusement park if her entry is drawn or if one of her two friends’ entries is drawn. That makes her have 3 favorable outcomes. This is the numerator. The fraction is the ratio.
  ::绘画中有50个条目, 因此有50个可能的结局。 分母是50个。 贝基可以去游乐园, 如果她被画入, 或者她的两个朋友的条目之一被画入。 这使得她有三个有利的结果。 这就是数字。 分数是比例 。

  $$\begin{array}{r}\frac{3}{50}\end{array}$$

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  Now, convert that to a decimal by dividing the numerator by the denominator.
  ::现在,通过将分子除以分母来转换成小数点。

  $\begin{array}{r}3÷50=.06\end{array}$

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  Then, convert .06 to a percent by moving the decimal two places to the right.
  ::然后,通过将小数点后两位移到右边,将 0.06 转换为 1% 。

  6%

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  That is the probability written as a ratio, decimal and percent.
  ::这是概率 写成一个比率, 小数点和百分比。

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  Example 2
  ::例2

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  Mrs. Scott placed the names of her 10 students in a bag. There were 6 girls’ names and 4 boys’ names in the bag. What is the probability that Mrs. Scott will not pull out a girl’s name? Write this answer as a decimal and a percentage.
  ::Scott夫人把10名学生的名字放在一个袋子里,包里有6名女孩的名字和4名男孩的名字,Scott夫人不会取出一个女孩的名字的可能性有多大?把这个答案写成小数和百分比。

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  First, write it as a ratio.
  ::首先,把它写成一个比例。

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  There 10 names in the bag, so there are 10 possible outcomes. The denominator is 10. There are 4 boy names in the bag. These are the  favorable outcome , so 4 is the numerator. This is the ratio.
  ::包里有10个名字, 所以有10个可能的结果。 分母是10。 包里有4个男孩的名字。 这些是有利的结果, 所以4个是分子。 这就是比例 。

  $$\begin{array}{r}\frac{4}{10}\end{array}$$

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  Next, convert this to a decimal by dividing the numerator by the denominator.
  ::下一步,将这个数字转换为小数点,将分子除以分母。

  $\begin{array}{r}4÷10=.40\end{array}$

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  Then, convert this to a percentage.
  ::然后,把这个转换成一个百分比。

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  .40 becomes 40% by moving the decimal two places to the right.
  ::将小数点后两位移到右侧,40将变为40%。

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  The answer is .40 or 40%.
  ::答案是40%或40%。

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  Example 3
  ::例3

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  Convert the fraction to a decimal and a percentage.
  ::将分数转换为小数点和百分比。

  $$\begin{array}{r}\frac{1}{4}\end{array}$$

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  First, divide the numerator by the denominator to get a decimal.
  ::首先,将分子除以分母以获得小数点。

  $\begin{array}{r}1÷4=.25\end{array}$

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  Next, convert the decimal to a percentage by moving the decimal two places to the right.
  ::下一步,将小数点转换为百分比,将小数点后两个位移到右边。

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  .25 becomes 25%
  ::25 成为25%

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  The answer is .25 or 25%.
  ::答案是25%或25%。

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  Example 4
  ::例4

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  Convert the fraction to a decimal and a percentage.
  ::将分数转换为小数点和百分比。

  $$\begin{array}{r}\frac{1}{2}\end{array}$$

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  First, divide the numerator by the denominator to get a decimal.
  ::首先,将分子除以分母以获得小数点。

  $\begin{array}{r}1÷2=.50\end{array}$

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  Next, convert the decimal to a percentage by moving the decimal two places to the right.
  ::下一步,将小数点转换为百分比,将小数点后两个位移到右边。

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  .25 becomes 25% by moving the decimal two places to the right.
  ::将小数点后的两个位移到右边,25 变为25%。

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  The answer is .5 or 50%.
  ::答案是5%或50%。

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  Example 5
  ::例5

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  Convert the fraction to a decimal and a percentage.
  ::将分数转换为小数点和百分比。

  $$\begin{array}{r}\frac{5}{8}\end{array}$$

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  First, divide the numerator by the denominator to get a decimal.
  ::首先,将分子除以分母以获得小数点。

  $\begin{array}{r}5÷8=.625\end{array}$

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  Next, convert the decimal to a percentage by moving the decimal two places to the right.
  ::下一步,将小数点转换为百分比,将小数点后两个位移到右边。

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  .625 becomes 62.5% by moving the decimal two places to the right.
  ::将小数点后两位移到右侧,625将变为62.5%。

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  The answer is .625 or 62.5%.
  
  ::答案是625或62.5%。

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  Review
  ::回顾

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  Without looking, you pull out one stone from the bag. A bag has the following 10 colored stones in it. There are 2 red ones, 2 blue ones, 3 green ones, 1 orange one, and 2 purple ones.
  ::袋子里有以下10块彩色的石头。有2块红色的,2块蓝色的,3块绿色的,1块橙色的,2块紫色的。

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  Write a decimal and a percent for each probability based on the scenario above.
  ::根据上述假设情况,为每种概率写一个小数和1%。

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  1. One orange stone
     ::一个橙色石头
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  2. A red stone
     ::红石
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  3. A green stone
     ::绿宝石
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  4. A yellow stone
     ::黄宝石
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  5. A blue stone or an orange one
     ::蓝石或橙石
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  6. A red one or a blue one
     ::红色的或蓝色的
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  7. A green one or an orange one
     ::绿色的或橙色的
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  8. A blue one or a green one
     ::蓝色的或绿色的
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  9. A blue one or a purple one
     ::蓝色或紫色
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  10. A purple one or a red one
      ::紫色的还是红色的
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  11. Not purple
      ::不是紫色
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  12. Not red
      ::不是红色
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  13. Not orange or purple
      ::不是橙色或紫色
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  14. Not red or purple
      ::不是红色或紫色
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  15. Not orange
      ::不是橙色

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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