6.7 识别补充物

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  Identifying the Complement 
  ::确定补充

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  The complement of an event is the sample space of all outcomes that are not the event in question. The complement of the event “a flipped coin lands on heads” is “a flipped coin lands on tails”. The complement of “A six-sided die lands on 1 or 2”. Is “A six-sided die lands on 3, 4, 5, or 6”. Complements are notated using the prime symbol ’ as in: $\begin{array}{r}P(A^{\mathrm{\prime }})\end{array}$ is the complement of $\begin{array}{r}P(A)\end{array}$ .
  ::活动的补充是所有结果的样本空间,这些结果不是有关事件, " 头顶上翻硬币地 " 的补充是 " 尾部翻硬币地 " , " 1或2号上六面死亡地 " 的补充是 " 3、4、5或6号上六面死亡地 " ,补充是 " 3、4、5或6号上六面死亡地 " ,补充是 " P(A) " 的补充。 P(A)是P(A)的补充。

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  The probability of the complement of an event is always whatever probability it would take to reach 100%. If the probability of pulling a green marble out of a bag is 26%, then the probability of the compliment (pulling a not green marble) is 74%.
  ::事件补充的概率始终是达到100%的概率。 如果从袋中拉出绿色大理石的概率为26%,那么赞美(拉出非绿色大理石)的概率为74%。

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  By convention, we most often see probabilities described as either a percentage or a fraction. Despite this, every calculated or experimental probability can be expressed as a value between 0 and 1 since percentages and fractions can all be converted to decimals and a probability must be between 0% and 100%. For example, a probability of  $\begin{array}{r}\frac{3}{4}\end{array}$ or 75% could also be expressed as the decimal .75, and a probability of 20% or  $\begin{array}{r}\frac{1}{5}\end{array}$ could be expressed as the decimal .20.
  ::按惯例,我们通常看到概率被描述为百分比或分数。 尽管如此,每个计算或实验概率都可以以0和1之间的值表示,因为百分比和分数都可以转换为小数点,概率必须介于0%和100%之间。例如,34或75%的概率也可以以小数点.75表示,20%或15的概率也可以以小数点.20表示。

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  One benefit of viewing probabilities as decimals is that it is easy to calculate the complementary probability of a given event by subtracting the event probability (expressed as a decimal) from 1.
  ::将概率视为小数点的一个好处是,很容易从1中减去事件概率(以小数点表示),从而计算出一个特定事件的补充概率。

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  Finding the Complement 
  ::查找补充

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  What is the complement to the event “Brian chooses one of the 2 red shirts from his drawer containing 10 shirts”?
  ::“Brian从抽屉中挑出含有10件衬衫的2件红衬衫之一”事件的补充是什么?

  

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  The complement would be the other possibility: “Brian chooses one of the not red shirts from his drawer.”
  ::补充物是另一种可能性:“Brian从抽屉中选择一种非红衬衫。”

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  Calculating Probability 
  ::计算概率

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  1. If the probability of randomly choosing a Queen from a standard deck of 52 cards is .077, what is the probability of the complementary event?
  ::1. 如果从52张牌的标准甲板上随机选择女王的概率是0.077,那么补充事件的概率是多少?

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  The complement would be choosing a card that is not a Queen, and the complement probability would be the difference between .077 and 1:
  ::补充是选择一张不是女王的卡片,补充概率是0.77和1:的差数。

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  $$\begin{array}{r}P(Quee{n}^{\mathrm{\prime }})=1-.077=.923\end{array}$$

  
  ::P(皇后)=1-0.77=.923

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  Therefore, the if the probability of choosing a Queen is 7.7%, then the probability of choosing a card not a Queen is 92.3%
  ::因此,如果选择皇后的概率为7.7%,那么选择卡片而不是皇后的概率为92.3%。

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  2. What is the probability of the compliment of the event: “Roll a standard die and get an even number”?
  ::2. 夸奖事件的几率是: " 标准死亡,获得偶数 " ?

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  There are three even numbers on a standard die: 2, 4, and 6. That means that the probability that you do roll and get an even number is:
  ::标准死亡数有三个偶数: 2, 4, 6, 也就是说,您真的滚动并获得偶数的概率是 :

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  $$\begin{array}{r}P(even)=\frac{3}{6}or50\mathrm{\%}\end{array}$$

  
  ::P(偶)=36或50%

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  Therefore, the complement is:
  ::因此,补充措施是:

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  $$\begin{array}{r}P(eve{n}^{\mathrm{\prime }})=1-.50=.5or50\mathrm{\%}\end{array}$$

  
  ::P(even_)=1-50=0.5%或50%

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  Earlier Problem Revisited
  ::重审先前的问题

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  The complement of an event is the set of all outcomes that are not the event.
  ::事件的补充是非事件的全部结果。

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  Examples 
  ::实例

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  Example 1
  ::例1

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  If $\begin{array}{r}P(X)=\frac{1}{6}\end{array}$ , what is $\begin{array}{r}P(X^{\mathrm{\prime }})\end{array}$ ?
  ::如果P(X)=16, 什么是P(X)?

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  $\begin{array}{r}P(X^{\mathrm{\prime }})=1-P(X)=1-\frac{1}{6}=\frac{5}{6}\end{array}$
  ::P(X)=1-P(X)=1-16=56

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  Example 2
  ::例2

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  What is the probability of the complement to a probability of 74%?
  ::74%的概率是多少?

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  The complement probability is  $\begin{array}{r}100\mathrm{\%}-74\mathrm{\%}=26\mathrm{\%}\end{array}$
  ::补充概率为1007426%

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  Example 3
  ::例3

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  What is the complement to the event: “flipped coin lands on heads”?
  ::事件的补充是:“头顶上抛掷硬币土地”吗?

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  "flipped coins land on tails"
  ::"抛掷的硬币落在尾巴上"

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  Example 4
  ::例4

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  What is the probability of the complement of randomly choosing one of the 3 quarters from a set of 10 coins?
  ::从一组10个硬币中随机选择三个季度中的四分之一的补丁概率是多少?

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  The event probability is  $\begin{array}{r}\frac{3quarters}{10coins}=\frac{3}{10}\end{array}$ . The complement is  $\begin{array}{r}1-\frac{3}{10}=\frac{7}{10}\end{array}$ .
  ::事件概率是 3 季度10 硬币= 310。补充是 1-310 = 710。

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  Example 5
  ::例5

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  What is the percent probability of  $\begin{array}{r}{Y}^{\mathrm{\prime }}\end{array}$ if $\begin{array}{r}\text{P(Y)}=\frac{1}{8}\end{array}$ ?
  ::如果P(Y)=18,Y的概率百分比是多少?

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  1. $\begin{array}{r}P(Y^{\mathrm{\prime }})=1-P(Y)=1-12.5\mathrm{\%}=87.5\mathrm{\%}\end{array}$
     ::PY`) = 1-P(Y) = 1 - 12.5 87.5%

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  Review 
  ::回顾

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  For problems 1 – 10, identify the percent probability of the complement of the described event.
  ::对于问题1 - 10, 确定补充所述事件的概率百分比。

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  1. Roll a standard die once and get an even number.
     ::滚动标准死亡一次 并获得一个偶数。
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  2. Pull a red card from a standard deck.
     ::从标准甲板上拉一张红牌
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  3. Pull a face card from a standard deck.
     ::从标准甲板上拉一张脸牌
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  4. Roll two standard dice and get a sum greater than 9.
     ::两张标准骰子 然后得到一个大于9的数
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  5. Pull two cards from a deck, without replacement, get at least one face card.
     ::从甲板上拉出两张牌,不更换,至少一张脸卡。
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  6. Roll a 10-sided die twice, get a 6 both times.
     ::滚动一个10面死亡两次, 得到一个6两次。
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  7. The probability that a student in your class likes chocolate is 34%.
     ::你们班的学生喜欢巧克力的概率是34%
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  8. Of the 76 students in your math class, 26 earned an A.
     ::在你数学班的76名学生中 26人挣了A
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  9. 23% of million-mile cars are Toyotas.
     ::23%的百万英里汽车是丰田汽车。
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  10. A candy machine has 24 green, 32 red, and 14 yellow candies in it. You choose a yellow candy.
      ::糖果机里有24个绿色的,32个红色的,14个黄色的糖果。你选一个黄色的糖果。
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  11. There are 150 students in your class, 40 have laptops, and 110 have tablets. 26 of those students have both a laptop and a tablet. What is the probability that a randomly chosen student has a tablet, given that she has a laptop?
      ::你们班级有150名学生,40名学生有笔记本电脑,110名学生有平板电脑。 其中26名学生有笔记本电脑和平板电脑。 随机选择的学生有平板电脑的可能性有多大,因为她有笔记本电脑?
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  12. Roll two standard dice, and get 4’s on both, given that you know that you have already rolled a 4 on one of them.
      ::并同时获得四分之一, 因为你知道你已经把四分之一放在其中之一上。
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  13. Draw two cards in a row, without replacement, that are the same suit from a standard deck.
      ::在一行中绘制两张牌, 不替换, 这是标准甲板上相同的西装 。
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  14. Roll of two standard dice once, getting a sum greater than 8, given that one of the dice is a 6.
      ::两个标准骰子滚动一次, 得到超过8的数, 因为一个骰子是6。

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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 。