11.15 利用模拟器探索实验概率

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  使用模拟来探索实验概率

  

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  Terry stood in front of the window and looked at the bicycle. It was perfect. She had debated all of the different options that she could have and still she thought that the one in the window of the bike shop was the perfect one for her.
  ::Terry站在窗前看着自行车,非常完美。她已经辩论了所有她可以选择的不同选择,她仍然认为自行车店的窗户是最适合她的。

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  “I have to have it,” she said smiling.
  ::她说,“我必须拥有它,”她笑着说。

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  “I guess you made up your mind,” Casey said.
  ::凯西说:“我猜你已经下定决心了。”

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  “Yes, imagine if we had asked all of our friends which bike I should get, we would have had a ton of different answers,” Terry said.
  ::”Terry说,“如果我们问过我们所有的朋友我应该买哪辆自行车,我们就会得到一吨不同的答案,”Terry说。

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  Terry is correct there would have been a lot of answers to keep track and tally.
  ::泰瑞是对的 有很多答案可以追踪和统计

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  Design a simulation where Terry would have surveyed her classmates and figured out the probability that she would have selected this bike out of the other 16 options.
  ::设计一个模拟 泰瑞会调查她的同学 并找出可能性 她会选择这辆自行车 在另外16个选项中。

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  In this concept, you will learn to use simulations to explore experimental probability.
  ::在此概念中,您将学会使用模拟来探索实验概率。

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  Simulations
  ::模拟模拟

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  A simulation is a way of collecting probability data using actual objects, such as coins, spinners, and cards.
  ::模拟是利用硬币、脊柱和卡片等实际物体收集概率数据的一种方法。

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

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  Conduct a simulation to see how many times heads comes up when you flip a coin 50 times.
  ::进行模拟, 以查看在翻硬币五十次时 有多少次头出现。

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  First, make a table like the one below. Conduct your simulation in groups of 10 flips. Leave lots of room to tally your results. Write in a prediction of how many times heads will turn up.
  ::首先, 绘制一张类似下面的桌子 。 以 10 个翻转组进行模拟 。 留下很多空间来计算您的计算结果 。 写一个预言, 预言有多少次会出现头部 。

  Trial	1	2	3	4	5	Prediction	Total
  Tally						$\begin{align*}X\end{align*}$	$\begin{align*}X\end{align*}$
  Heads						25
  Total Flips						50

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  Second, begin conducting your simulation. Tally your results. Some sample data is shown. Remember, this is a sample and not actual data.
  ::其次,开始进行模拟。 输出结果。 显示一些样本数据。 记住, 这是一个样本, 而不是实际数据 。

  Trial	1	2	3	4	5	Prediction	Total
  Tally	$\begin{align*}||||\end{align*}$	$\begin{align*}\cancel{||||}\end{align*}$	$\begin{align*}|||\end{align*}$	$\begin{align*}\cancel{||||} \ |\end{align*}$	$\begin{align*}\cancel{||||}\end{align*}$	$\begin{align*}X\end{align*}$	$\begin{align*}X\end{align*}$
  Heads						25
  Total Flips	10	10	10	10	10	50

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  Then, fill in the rest of your table.  Here is what your completed table might look like.
  ::然后填满你剩下的桌子。这就是你填满的桌子可能的样子。

  Trial	1	2	3	4	5	Prediction	Total
  Tally	$\begin{align*}||||\end{align*}$	$\begin{align*}\cancel{||||}\end{align*}$	$\begin{align*}|||\end{align*}$	$\begin{align*}\cancel{||||} \ |\end{align*}$	$\begin{align*}\cancel{||||}\end{align*}$	$\begin{align*}X\end{align*}$	$\begin{align*}X\end{align*}$
  Heads	4	5	3	6	5	25	23
  Total Flips	10	10	10	10	10	50	50

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  Now that you are set up and understand the process, run the simulations and solve the problems that follow. Record your data. Make sure you make a table and predictions for each simulation.
  ::现在您已经设置并了解了过程, 运行模拟并解决了随后的问题。 记录您的数据。 请确保您为每次模拟都给出表格和预测 。

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  Let’s look at another example.
  ::让我们再看看另一个例子。

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  Run a simulation of 60 coin flips to see how frequently tails turns up.
  ::模拟60枚硬币的翻转 以观察尾巴的出现频率

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  1. How many times did you predict tails would occur? How many times did it actually occur?
     ::你预测了多少次尾巴会发生?
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  2. How well did your data agree with your prediction? Explain.
     ::你的数据与你的预测有多么一致?

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  Work on this simulation with a partner. Record your data and then discuss your answers.
  ::与合作伙伴一起进行模拟。 记录您的数据, 然后讨论您的答案 。

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  Many calculators and websites have random number generators and other features that can be used to generate data for simulations. Here you will use the website to run a coin flipping simulation.
  ::许多计算器和网站有随机数生成器和其他功能,可用于生成模拟数据。您将在这里使用网站运行硬币翻转模拟 。

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  First, make a table for collecting coin flip data like the one shown. Fill in your prediction. You won’t need to tally data here –the computer will do it for you.
  ::首先,为收集硬币翻转数据绘制一张表格,像所显示的那样。填满你的预测。你不需要在这里计算数据 — — 电脑会为你做。

  Trial	1	2	3	4	5	6	7	8	9	10	Prediction	Total
  Heads
  Total Flips

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  Next, open the webpage . Click on “coin flipper.” Here you selected 10 as the number of coins to flip on each trial. Click on “Flip coin(s)”. Record the data in the table. Sample data collected from the website is shown below.
  ::下一步,打开网页。单击“纸币翻转器 ” 。 在这里,您选择了 10 个硬币作为每次试金币翻转的硬币数,单击“硬币翻转” , 记录表格中的数据。 从网站收集的样本数据见下文。

  Trial	1	2	3	4	5	6	7	8	9	10	Prediction	Total
  Heads	6	4	6	2	7	6	6	5	5	5	50	52
  Total Flips	10	10	10	10	10	10	10	10	10	10	100	100

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  Then, analyze your data. How accurate was your prediction?
  ::那么分析你的数据 你预测的准确度如何?

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  The prediction was that there is a 50% chance of flipping heads. After doing 100 trials, the simulation showed that 52% of the time, the coin flipped heads.
  ::预测是有50%的翻头机会。在做了100次试验后,模拟显示52%的时间,硬币翻头。

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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  Terry and the bike. Terry needs to conduct a simulation to conduct a survey of her classmates on what bike they would recommend of the 16 different options.
  ::早些时候,你遇到了关于Terry和自行车的问题。Terry需要进行模拟,对同学们进行调查,了解他们建议16种不同选择中的自行车是什么。

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  First, to accomplish this task, Terry could write out all of the 16 options for bicycles. Then she could go around and ask her friends to rate the bikes 1, 2 or 3. One being the first choice etc.
  ::首先,为了完成这项任务,Terry可以写出所有16种自行车的选项。 然后她可以到处叫朋友给1、2或3辆自行车打分,其中1辆是首选车等。

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  Next, Terry could calculate her scores and narrow it down to the bikes that received the most votes. The bicycle that was selected the most times would be the winning bike.
  ::接下来,泰瑞可以计算她的分数,缩小到获得最多选票的自行车。 最常被选中的自行车就是获胜的自行车。

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  Example 2
  ::例2

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  Jessie decided to conduct an experiment with a spinner. The spinner is divided into four colors: red, blue, orange and green. Jessie predicted that out of 30 spins that the spinner would be red 10% of the time.
  ::杰西决定与一个旋翼者进行实验。 旋翼者分为四种颜色: 红色、 蓝色、 橙色和绿色。 杰西预测,在30个旋转中, 旋翼者占10%的时间是红色的。

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  She conducted the experiment and the spinner was red four times. Is her prediction correct?
  ::她进行了实验 脊柱是红色的4次 她的预测正确吗?

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  First, to figure this out, you must first write a probability and then compare it to the 10% that Jessie predicted. The actual result is that the spinner was red 4 out of 30 times.
  ::首先,要弄清楚这一点,你必须先写出一个概率,然后把它与杰西预测的10%的概率进行比较。实际结果是,30倍中脊柱是红色的4倍。

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  $$\begin{align*}P(\text{red})= \frac{4}{30}\end{align*}$$
  ::P(red)=430

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  Second, convert to a percent .
  ::第二,转换成百分之一

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  $$\begin{align*}\begin{array}{rcl} P(\text{red}) &=& \frac{4}{30} \\ P (\text{red}) &=& 0.133 \\ P (\text{red}) &=& 13.3 \% \end{array}\end{align*}$$
  ::P(red)=430P(red)=0.133P(red)=13.3%

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  The answer is 13.3%.
  ::答案是13.3%。

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  Jessie’s prediction was too low. The actual result was higher than 10%.
  ::杰西的预测太低了。 实际结果超过10%。

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  Example 3
  ::例3

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  Is the following statement true or false?
  ::下列声明是真实的还是虚假的?

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  A simulation is an experiment.
  ::模拟是一种实验。

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  This statement is true.
  ::这一说法是真实的。

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  Example 4
  ::例4

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  Is the following statement true or false?
  ::下列声明是真实的还是虚假的?

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  To explore experimental probability, you could simply spin a spinner one time.
  ::要探索实验概率, 你可以只旋转一个旋转器一次。

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  This statement is false. You need to have more than one trial in an experiment to be exploring experimental probability.
  ::此语句是虚假的。 您需要在实验中进行多个试验, 才能探索实验概率 。

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  Example 5
  ::例5

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  Is the following statement true or false?
  ::下列声明是真实的还是虚假的?

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  To use a coin in a simulation, you would need to flip the coin many, many times.
  ::要在模拟中使用硬币, 你需要翻翻硬币很多很多次。

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  This statement is true.
  ::这一说法是真实的。

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  Review
  ::回顾

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  Run a simulation using playing cards. Make a stack of the Ace, Jack, King, Queen, and Ten of each suit. Predict how frequently an Ace will turn up. Run 60 trials in groups of 10. Return the card to the deck and shuffle after you choose each card. Use a table like the one below.
  ::使用游戏卡进行模拟。 制作一张A、 Jack、 King、 Queen 和 10 套西装中的A、 Jack、 King、 Queen 和 10套。 预测一个A的出现频率。 运行60次10组的测试。 在您选择每张牌后, 将牌返回甲板和洗牌。 使用下面的桌子 。

  Trial	1	2	3	4	5	6	Prediction	Total
  Tally
  Ace
  Total tosses	10	10	10	10	10	10

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  1. How many times did you predict an Ace would occur? How many times did it actually occur?
     ::你预测过多少次A会发生?
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  2. How well does your data agree with your prediction?
     ::你的数据如何同意你的预测?

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  Run a simulation using playing cards. Make a stack of the Ace, Jack, King, Queen, and Ten of each suit. Predict how frequently a King, a Queen and a Jack will turn up. Run 60 trials in groups of 10. Return the card to the deck and shuffle after you choose each card. Use a table like the one below.
  ::使用游戏卡进行模拟。 制作一张A、 Jack、 King、 Queen 和 10 套西装中的A、 Jack、 King、 Queen 和 10套。 预测国王、 女王和 Jack 的出现频率 。 运行60 个10 组的试验 。 在您选择每张牌后, 将牌返回甲板和洗牌。 请使用下面的桌子 。

  Trial	1	2	3	4	5	6	Prediction	Total
  Tally
  Ace
  Total tosses	10	10	10	10	10	10

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  3. How many times did you predict an King would occur? How many times did it actually occur?
  ::3. 你预测国王会发生多少次,实际发生多少次?

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  4. How many times did you predict a Jack would occur? How many times did it actually occur?
  ::4. 你预测杰克会发生多少次,实际发生多少次?

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  5. How many times did you predict a Queen would occur? How many times did it actually occur?
  ::5. 你预测皇后会发生多少次,实际发生多少次?

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  6. How well does your data agree with your prediction?
  ::6. 贵国的数据如何同意你的预测?

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  Run a simulation of 72 number cube tosses in groups of 12 to see how frequently 4 or 5 turns up. Use a table like the one below.
  ::运行一个由 72 个立方体的 十二组抛掷的模拟, 以查看 4 或 5 的频率。 使用下面的表格 。

  Trial	1	2	3	4	5	6	Prediction	Total
  Tally
  4 Or 5
  Total tosses	12	12	12	12	12	12

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  7. How many times did you predict 4 or 5 would occur? How many times did it actually occur?
  ::7. 你预测4或5起事件会发生多少次,实际发生多少次?

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  8. How well does your data agree with your prediction?
  ::8. 贵国的数据如何同意你的预测?

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  9. Try another group of 36 tosses. Add your results of 36 tosses to your previous 72 tosses to make 108 total tosses. How well did your data now agree with your prediction? Explain.
  ::9. 尝试再试一组36个索斯。将36个索斯的结果添加到先前的72个索斯中,以得出108个总索斯。你的数据现在与你的预测有多一致?请解释。

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  Use for each simulation. Run a number cube simulation to see how many times each number on the cube comes up. In , click on the link that reads “dice roller”. Choose 12 for the number of number cubes (dice) you want to roll. Set up a table like the one below to have a total of 96 rolls.
  ::用于每次模拟 。 运行一个数字立方体模拟, 以查看立方体上每个数字的倍数。 在 中, 单击“ 滚动滚动” 的链接 。 您想要滚动的立方体数( 骰子) 选择 12 个 。 设置一个像下面的表格, 总共可以有 96 个滚动 。

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  Tally up the number of 1s, 2s, 3s, 4s, 5s, and 6s that turn up and record them in the table. Keep rolling until you have a total of 96 rolls.
  ::将一号、二号、三号、四号、五号和六号的号码调高, 并把它们记录在桌子上。 继续滚动, 直到你总共有96卷。

  Number	1	2	3	4	5	6	Total
  Tally
  Total							96
  Prediction	16	16	16	16	16	16	96

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  10. How many times did you predict each number on the number cube would appear in 96 rolls?
  ::10. 你预测了96卷的立方体上每个数字会出现多少次?

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  11. How many times did it actually appear?
  ::11. 它实际出现多少次?

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  12. How well does your data agree with your prediction?
  ::12. 贵国的数据如何同意你的预测?

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  13. Try an additional 96 rolls. How did the additional data change your results? Explain.
  ::13. 再试一个96卷。补充数据是如何改变你的结果的?解释。

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  Now design your own simulation and use a spinner or two number cubes.
  ::现在设计你自己的模拟,然后使用一个螺旋体或两个数字立方体。

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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 。