概率的补规则

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The middle school’s spring carnival was starting right after school, so Cheryl sat impatiently in class waiting for the bell to ring. Her goal was to be one of the first students in line for the cake walk, which was sort of like playing musical chairs. In the cake walk, 20 students walk around a numbered circle and stop on the closest number when the music stops. The caller then draws a number, and whoever is standing on that number wins a cake of their choice. Cheryl has her heart set on winning a chocolate cake. If Cheryl has a 5% chance of ending up on the selected number, what is the  probability  that she will not end up on the selected number?
::中学春季嘉年华会开学后, 谢丽尔在课堂上不耐烦地等待钟声响起。 她的目标是成为最早排队参加蛋糕散步的学生之一,这就像玩音乐椅一样。 在蛋糕散步中,20名学生环绕一个编号的圆圈,在音乐停止时停靠最接近的数字。 打电话者然后抽出一个数字, 站在数字上的人会赢得他们自己选择的蛋糕。 谢丽尔的心被安排在赢得巧克力蛋糕上。 如果谢丽尔有5%的机会结束选定数字,那么她不会最后达到选定数字的可能性有多大?

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In this concept, you will learn how to find the probability of  complementary events .
::在这个概念中,你将学会如何找到发生互补事件的概率。

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Finding Probability of Complementary Events
::寻找补充活动的可能性

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When you know the likelihood that something will happen, you can determine or base your actions on that  event  happening. If you knew today was going to be a sunny day or a rainy day, and the weather report stated there was a 10% chance of rain, you can figure out the  complementary event  or the opposite probability, which would be 90% chance of sun. If there is a 10% chance that it will not be sunny, then there is a 90% chance that it will be sunny.
::当您知道某事可能发生时,您可以确定或根据该事件发生时的行动。如果您知道今天是阳光明媚的一天或雨天,而且天气报告显示有10%的降雨机率,您可以找出补充事件或相反的概率,即90%的太阳机率。如果10%的概率不是阳光晴朗,那么90%的概率是阳光晴朗。

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Here is another way to look at complements. In the following statement,  $\begin{array}{r}P(A)\end{array}$  means the “probability of  $\begin{array}{r}A\end{array}$ ” and  $\begin{array}{r}P(B)\end{array}$  is the “probability of  $\begin{array}{r}B\end{array}$ .”
::另一种观点是补充性。 在下面的语句中,P(A)意指“A的可能性 ” , P(B)意指“B的可能性 ” 。

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If  $\begin{array}{r}A\end{array}$  and  $\begin{array}{r}B\end{array}$  are complements, then  $\begin{array}{r}P(B)=100\mathrm{\%}-P(A)\end{array}$ . For example, if the probability of  $\begin{array}{r}A\end{array}$ ,  $\begin{array}{r}P(A)\end{array}$  is 10%, then the probability of  $\begin{array}{r}B\end{array}$ ,  $\begin{array}{r}P(B)\end{array}$  is  $\begin{array}{r}100\mathrm{\%}-10\mathrm{\%}\end{array}$ , which is 90%.
::如果A和B是补充性的,则P(B)=100%-P(A)。例如,如果A、P(A)的概率为10%,那么B、P(B)的概率为100%-10%,即90%。

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Here is an example.
::举一个例子。

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Write the complementary event for the probability shown here.
::写入此处显示的概率的补充事件 。

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“There is a 50% chance that Mary will be coming over on Saturday.”
::“玛丽有50%可能周六会来。”

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First, look at the opposite probability.
::首先,看看相反的概率。

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There is a 50% chance that Mary will be coming over, so there is a 50% chance that she will not be coming over.
::玛丽有50%的希望会来 所以有50%的希望不会来

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Next, write the complementary event, which is the opposite probability.
::接下来,写下补充事件,这是相反的概率。

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“There is a 50% chance that Mary will not be coming over.”
::“有50%的可能性,玛丽不会过来。”

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You can write complementary events as fractions, decimals and percents. Use whatever form is used in the example and have the complementary event match that form.
::您可以以分数、小数和百分数的形式写入补充事件。使用示例中使用的任何形式,并让补充事件与该形式相匹配。

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Sometimes, when it comes to determining the probability of an event, you just need to use common sense and ask yourself if the event is likely to occur, unlikely to occur, certain to occur, or is impossible. One way to do this is by looking at the complementary event. The more likely the complementary event is, then the less likely the original situation will be.
::有时,当涉及到确定事件发生概率时,你只需要使用常识,问问自己该事件是否可能发生、不可能发生、一定发生或不可能发生。 一种方法就是查看补充事件。 补充事件的可能性越大,最初的情况就越不可能发生。

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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 and her quest for a chocolate cake.
::早些时候,有人给了你一个问题 关于Cheryl和她对巧克力蛋糕的追求。

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Cheryl is third in line when Mrs. Mixon and Jackie open the cake walk. She pays her $1 then takes her place on the circle with the other 19 students. There are 20 numbers on the circle, so each student will end up on a number. That means she has a 1 in 20 chance of winning, which is a 5% probability. Cheryl begins to think she just wasted $1when she considers the odds of her losing.
::当Mixon和Jackie夫人打开蛋糕散步时,Cheryl排在第三位。她付给她一美元,然后她与其他19名学生一起在圆圈中占有一席之地。圆圈里有20个数字,所以每个学生最后都会有一个数字。这意味着她有一个20分之一的赢机会,这是5%的概率。Cheryl开始认为她只是浪费了1美元,当她认为她有可能输的时候。

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First, consider the opposite probability of Cheryl winning.
::首先,考虑谢丽尔获胜的概率

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She will lose because she won’t end up on the selected number.
::她会输, 因为她不会在所选的号码上落地。

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Next, subtract the probability she will win, which is 5%, from 100% to get the probability that she will lose.
::接下来,从100%中减去她赢的概率,即5%, 以获得她输的概率。

95%

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There is a 95% chance that Cheryl will lose.
::Cheryl有95%的几率会输

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Example 2
::例2

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Write a complementary event for the following situation.
::为下列情况编写补充活动。

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The boy has a 40% chance of winning the race.
::男孩有40%的机会赢得比赛

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First, consider the opposite probability, which is the boy losing the race.
::首先,考虑相反的概率, 就是输掉比赛的男孩。

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Next, subtract 40% from 100% to get the probability of the boy losing.
::接下来,从100%中减去40%, 以获得男孩输的概率。

60%

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There is a 60% chance the boy will lose the race.
::男孩有60%的机会输掉比赛

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Example 3
::例3

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Write a complementary event for the following situation.
::为下列情况编写补充活动。

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The course has a 74% passing rate.
::该课程的通过率为74%。

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First, consider the opposite probability, which is the failure rate.
::首先,考虑相反的概率,即失败率。

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Next, subtract 74% from 100% to get the failure rate.
::接下来,从100%中减去74% 以获得故障率。

26%

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The course has a 26% failure rate.
::课程有26%的失败率。

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Example 4
::例4

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Write a complementary event for the following situation.
::为下列情况编写补充活动。

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There is a 90% chance that Teddy will pass the driver’s exam on his first try.
::Teddy在第一次考试时通过驾驶考试的可能性是90%。

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First, consider the opposite probability, which is Teddy failing on his first try.
::首先,考虑相反的概率, 那就是泰迪在第一次尝试时失败了。

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Next, subtract 90% from 100% to get the failure rate.
::接下来,从100%中减去90%, 以获得失败率 。

10%

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There is a 10% chance that Teddy will fail on his first try.
::泰迪第一次尝试失败的可能性是10%

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Example 5
::例5

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Write a complementary event for the following situation.
::为下列情况编写补充活动。

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There is a 20% chance that it will snow tonight.
::今晚下雪的可能性是20%

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First, consider the opposite probability, which is, it won’t snow.
::首先,考虑相反的概率,也就是说,它不会下雪。

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Next, subtract 20% from 100% to get the probability that it won’t snow.
::接下来,从100%中减去20%,以获得它不会下雪的概率。

80%

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There is an 80% chance that it won’t snow.

::百分之八十的概率不会下雪。

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Review
::回顾

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Use common sense and make a prediction. Use likely, impossible, unlikely, or certain to describe each statement.
::使用常识并作出预测。 使用可能、不可能、不可能或肯定描述每个声明。

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1. Our team has a perfect record. It is _______ that we will win on Saturday.
::1. 我们的团队有完美的记录,我们星期六将赢得胜利。

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2. A baby born will either be a boy or a girl.
::2. 出生的婴儿要么是男孩,要么是女孩。

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3. A pig will fly through the sky.
::3. 一只猪将飞过天空。

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4. A cat will like a dog.
::4. 猫会喜欢狗的。

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5. There is an 85% chance it will rain. It is _______ that it will rain.
::5. 降雨的概率为85%,下雨的概率为85%。

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Find the complement’s percentage.
::寻找补丁的百分比 。

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6.  $\begin{array}{r}A\end{array}$  and  $\begin{array}{r}B\end{array}$  are complements.  $\begin{array}{r}P(B)=15\mathrm{\%}\end{array}$ . Find  $\begin{array}{r}P(A)\end{array}$ .
::6. A和B是补充。P(B)=15%。查找P(A)

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7.  $\begin{array}{r}C\end{array}$  and  $\begin{array}{r}D\end{array}$  are complements.  $\begin{array}{r}P(C)=80\mathrm{\%}\end{array}$ . Find  $\begin{array}{r}P(D)\end{array}$ .
::7. C和D是补充。P(C)=80%。查找P(D)

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8.  $\begin{array}{r}G\end{array}$  and  $\begin{array}{r}H\end{array}$  are complements.  $\begin{array}{r}P(H)=49\mathrm{\%}\end{array}$ . Find  $\begin{array}{r}P(G)\end{array}$ .
::8. G和H是补充。P(H)=49%。查找P(G)

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9.  $\begin{array}{r}T\end{array}$  and  $\begin{array}{r}S\end{array}$  are complements.  $\begin{array}{r}P(T)=33\mathrm{\%}\end{array}$ . Find  $\begin{array}{r}P(S)\end{array}$ .
::9. T和S是补充。 P(T)=33%。 Find P(S)

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10.  $\begin{array}{r}L\end{array}$  and  $\begin{array}{r}K\end{array}$  are complements.  $\begin{array}{r}P(K)=70\mathrm{\%}\end{array}$ . Find  $\begin{array}{r}P(L)\end{array}$ .
::10. L和K是补充。 P(K) = 70%。 Find P(L) 。

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11.  $\begin{array}{r}A\end{array}$  and  $\begin{array}{r}B\end{array}$  are complements.  $\begin{array}{r}P(B)=12\mathrm{\%}\end{array}$ . Find  $\begin{array}{r}P(A)\end{array}$ .
::11. A和B是补充。 P (B) = 12%。 Find P (A) 。

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12.  $\begin{array}{r}N\end{array}$  and  $\begin{array}{r}M\end{array}$  are complements.  $\begin{array}{r}P(N)=96\mathrm{\%}\end{array}$ . Find  $\begin{array}{r}P(M)\end{array}$ .
::12. N和M是补充。 P(N)=96%。 Find P(M)=96%。

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13.  $\begin{array}{r}Q\end{array}$  and  $\begin{array}{r}Z\end{array}$  are complements.  $\begin{array}{r}P(Q)=10\mathrm{\%}\end{array}$ . Find  $\begin{array}{r}P(Z)\end{array}$ .
::13. Q和Z是补充。P(Q)=10%。查找P(Z)

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Determine whether the two events are complementary or not complementary.
::确定这两个活动是否相辅相成。

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14. Percentage of votes that 2 candidates get in a 2-candidate election
::14. 2名候选人在2名候选人选举中获得的选票百分比

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15. Percentage of votes that 2 candidates get in a 3-candidate election
::15. 2名候选人在3天选举选举中获得的选票百分比

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16. Winning a game or losing a game
::16. 赢一场游戏或输一场游戏

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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