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  • 利用模拟来估计复合事件概率

    In This Lesson
    ::在本课程中

    You will apply  the process for running simulations from    to  compound events.  You may want to review the information from previous lesson on setting up simulations.
    ::您将应用此程序运行从复合事件到复合事件的模拟程序。 您可能想要查看先前关于设置模拟的课程中的信息 。

    To set up a simulation ,  determine what event you want to simulate, describe the possible outcomes , and link each outcome to one or more random numbers. Then, choose a source of random numbers (coin, die, deck of cards, or computer program) and begin your simulation . For compound events, y ou will need to organize your data differently in order to take into account multiple events within the simulation. 
    ::要设置模拟, 确定您想要模拟的事件, 描述可能的结果, 并将每个结果与一个或多个随机数字链接。 然后, 选择随机数字的来源( coin, die, 牌牌甲板, 或计算机程序) 并开始模拟。 对于复合事件, 您需要以不同的方式组织您的数据, 以便考虑到模拟中的多个事件 。

     

    Boys or Girls?
    ::男孩还是女孩?

    A young couple is excited to start a family. They plan to have  4 children. What is the  probability that they will have 2 boys and 2 girls?
    ::一对年轻夫妇为组建家庭感到兴奋,他们计划有4个孩子。他们有2个男孩和2个女孩的可能性有多大?

    Use a simulation of 50 trials to  estimate the probability of this compound event. For this simulation, you will use a coin to represent one child, where heads = girls, and tails = boys. Each trial will have 4  coin flips (to represent the four children), so 50 trials will have 200 flips .
    ::使用50个试验的模拟来估计这个复合事件的概率。 对于这个模拟, 您将使用一枚硬币来代表一个孩子, 头部代表女孩, 尾部代表男孩。 每次试验将有四枚硬币( 代表四个孩子 ) , 所以50枚试验将代表200个硬币 。

    Use the  interactive  to keep track of your results in the table. Then answer the questions that follow.
    ::使用交互方式在表格中记录您的结果。 然后回答下面的问题 。

     

    INTERACTIVE
    Compound Coin Toss
    minimize icon

    You are simulating 50 trials where you need to flip a coin 4 times for every trial.
    ::你模拟了50个审判, 每次审判都需要翻4次硬币。

    • Click the button to flip the coin and record the results.
      ::单击按钮翻转硬币并记录结果。
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    Discussion Question
    ::讨论问题

    How does the estimated probability from your simulation compare to the theoretical probability of having 2 boys and 2 girls? Why might your classmates have different simulation results than you?
    ::模拟的概率与有2个男孩和2个女孩的理论概率相比如何? 为什么同学的模拟结果与你不同?

     

    Travel Plans
    ::旅行旅行计划

    A family of five is planning a big summer vacation. Each member of the family wants to go to a different city: Paris, Rome, Barcelona, Tallinn , and Berlin; however, they only have enough time for 3 cities. In order to decide, they will throw darts at a map and the first three cities they hit are where they will go.
    ::五口之家正在计划一个大暑假,每个家庭成员都想去另一个城市:巴黎、罗马、巴塞罗那、塔林和柏林;然而,他们只有三座城市的足够时间。 为了决定,他们将把飞镖扔到地图上,头三个被击中的城市是他们要去的地方。

    You are going to perform a simulation with 50 trials. Instead of throwing actual darts, you will use three dice to represent the three cities hit by darts. Start by answer the questions to determine how to approach the simulation.
    ::您将用50次试验来进行模拟。 您将使用三骰子来代表被飞镖击中的三个城市。 首先回答问题, 以确定如何接近模拟 。

     

     

    Note that each event only has 5 outcomes, so you will not use the 6th side of the die. If you happen to roll a 6, it will not be counted and you will have to roll again.
    ::请注意每个事件只产生5个结果, 所以您不会使用死亡的第六侧。 如果您碰巧滚动了 6, 它将不会被计算, 您将不得不再次滚动 。

    Each trial needs three rolls to represent the three cities. Order does not matter because the family will arrange travel plans based on flights and where the cities are relative to each other.
    ::每个试验都需要三个卷来代表这三个城市。 秩序无关紧要,因为家属将根据航班安排旅行计划,而且城市彼此相对。

    Use the interactive to perform the simulation with 50 trials. Then answer the questions that follow.
    ::使用交互程序进行模拟, 进行50次试验。 然后回答下面的问题 。

     

    INTERACTIVE
    Compound Events with Dice
    minimize icon
    • Use the Dotplot/Key button to switch views.
      ::使用 Dotplot/ Key 按钮切换视图 。
    • Click on Roll to simulate rolling three dice. You will simulate up to 50 trials.
      ::点击滚动以模拟滚动 3 骰子。 您将模拟多达 50 个试验 。
    • The outcome that corresponds to those dice will get a point above its initials. 
      ::与这些骰子相对应的结果将获得高于其首字母的点数。
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    Discussion Question
    ::讨论问题

    Compare the probability from the simulation to the  actual results (refer to Question 6).  Why might the simulation of rolling dice not be an appropriate model of throwing darts at a map?
    ::将模拟的概率与实际结果进行比较(参见问题6)。 为什么滚骰的模拟不能成为向地图投掷飞镖的适当模型?

    Make a Simulation
    ::模拟模拟

    In the previous lesson you chose an event and created a simulation to model its probability. Appropriate tools were chosen to model the probability of the event. Either extend your scenario to model a compound event or choose a new scenario. Aim for a minimum of 3 simple events . Consider whether the events are dependent or independent. State the scenario, the probabilities, the research you did, and the simulation tools you chose.
    ::在上一个课程中,您选择了一个事件,并创建了一个模拟来模拟其概率。选择了适当的工具来模拟事件的概率。或者扩展您的假设情景来模拟复合事件,或者选择新的假设情景。至少瞄准3个简单事件。考虑事件是依附还是独立。请说明假设情景、概率、你所做的研究以及你选择的模拟工具。

     Summary
    ::摘要

    • To create a simulation, determine what event you want to simulate, describe the possible outcomes, and link each outcome to one or more random numbers. Then, choose a source of random numbers (coin, die, deck of cards, or computer program) and begin your simulation.
      ::要创建模拟, 确定您想要模拟什么事件, 描述可能的结果, 并将每个结果链接到一个或多个随机数字 。 然后选择随机数字的来源( coin, die, 牌甲板, 或计算机程序) 并开始模拟 。
    • Pay close attention to whether order matters or not when determining the total number of outcomes.
      ::在确定结果总数时,密切注意顺序是否重要。