章节大纲

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  • 介绍化合物概率

    In This Lesson
    ::在本课程中

    Y ou will expand your knowledge of probability and determine what happens when more than one event occurs. Sometimes, these events are dependent upon each other; drawing one card out of a deck, then another. Sometimes they are independent ; rolling a die and then flipping a coin. When two events are independent, they have no relation to each other and they do not a ffect each other. When two events are dependent, one event depends on the other.  For example, when  drawing cards from a standard deck, the second  card depends on the first, because there is one less card in the pile when you draw the second time. 
    ::您将扩大对概率的了解, 并确定发生不止一个事件时会发生什么。 有时, 这些事件彼此依赖; 从甲板上画一张牌, 然后从另一张牌上画一张。 有时, 它们独立; 滚动一个死板, 然后翻一个硬币。 当两个事件是独立的时, 它们彼此之间没有关系, 它们不会相互影响。 当两个事件是独立的时, 一个事件取决于另一个事件。 例如, 当从一个标准甲板上画牌时, 第二张卡片取决于第一个牌, 因为第二次画的时候, 堆叠中的牌少了一个。

    D ependent and   can both be  compound events , because there is more than one event involved in  the same final outcome .
    ::由于同一最后结果涉及不止一个事件,因此既属于依赖性事件,也可能是复合事件。

     

    Car Options
    ::car 选项选项

    Milo is looking to buy a new car. He is debating between a sedan or an SUV.  He likes red, navy blue , charcoal grey, or black for the exterior color and black or grey for the interior color.  How many different cars choices are there?
    ::Milo想买一辆新车。 他正在一辆轿车或一辆SUV之间辩论。 他喜欢红色、海军蓝色、木炭灰色或黑色的外色, 内部颜色是黑色或灰色的。 有多少不同的汽车选择?

    Use the blank tree diagram to determine how many different car choices there are.  Select from the car  types, exterior colors, and interior colors  i n the diagram. The first level is  the car type, the second  level is  the exterior color, and the last  level is the interior color.
    ::使用空白树图来确定有多少不同的汽车选择。 从图表中的汽车类型、外部颜色和内部颜色中选择。 第一层是汽车类型, 第二层是外部颜色, 最后一层是内部颜色 。

     

    INTERACTIVE
    Car Options
    minimize icon
    • Use the dropdown menu to make a tree of different combination of cars. More branches will appear as you fill out the tree.
      ::使用下拉菜单来制作一棵不同的汽车组合树。 在您填满树时, 将会出现更多的树枝 。
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    robability-of-compound-events" quiz-url="https://www.ck12.org/assessment/ui/embed.html?test/view/5f4558cf541213598eba9ae4&collectionHandle=probability&collectionCreatorID=3&conceptCollectionHandle=probability-:吐舌头robability-of-compound-events&mode=lite" test-id="5f4558cf541213598eba9ae4">

     

    To find the total number of outcomes , you need to multiply the number of possible outcomes from each event together. As you already know from using the commutative law in the past , order does not matter with multiplication and  so will not matter when determining the total number of outcomes for compound events.
    ::要查找结果的总数, 您需要将每个事件的可能结果数一起乘以。 正如您过去使用通货法时已经知道的那样, 秩序与乘法无关, 在确定复合事件结果总数时也无关紧要 。

     

    Make I t Your Way
    ::做你的路

    The Full Belly Deli makes sandwiches to order.  They have 4 different types of bread (wheat, white, rye, and sourdough), 4 different types of meat (turkey, roast beef, pastrami, and ham), and 2 condiments (mayo and mustard).  If you pick one from each category, how many different sandwiches could you order?
    ::贝利·德利(Belly Deli)制成三明治。它们有四种不同种类的面包(小麦、白麦、黑麦和酸奶),四种不同种类的肉类(木薯、烤牛肉、意大利面条和火腿)和两种调味品(马约和芥末)。如果你从每类中挑一个,你可点多少种不同的三明治?

    Use the interactive to place each type of bread (square in the middle), meat (circle), and condiment (smaller square ) in the diagram to determine how many different types of sandwiches can be made.  Then, answer the  interactive questions below. 
    ::使用交互方式将每种面包(中间方形)、肉类(圆圈)和调味品(小方形)放在图表中,以确定可以做多少种不同的三明治。然后回答以下交互问题。

     

    INTERACTIVE
    Make It Your Way
    minimize icon

    You are ordering a sandwich at a shop and you would like to know every possible sandwich that you  could order. The sandwich shop offers:  3  different kinds of bread,  4  different kinds of meat, and  2   different kinds of condiments. Each sandwich must have one type of bread, meat and condiment.

    ::您正在商店订购三明治,您想知道您可以订购的每一个可能的三明治。三明治店提供三种不同的面包、四种不同的肉类和两种不同的调味品。每个三明治必须有一种面包、肉类和调味品。

    Drag the ingredients into the trees given to see all the possible combinations.

    ::将元素拖放到给定的树上以查看所有可能的组合。

    • Drag the breads into the large brown squares
      ::将面包拖到大棕色方形
    • Drag the meats into the brown  circles
      ::将肉肉拖入棕色圆圈
    • Drag the condiments into the small brown squares 
      ::将调味调味物拖到小棕色方形
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    robability-of-compound-events" quiz-url="https://www.ck12.org/assessment/ui/embed.html?test/view/5f4558d5b6df72a2bcdbf276&collectionHandle=probability&collectionCreatorID=3&conceptCollectionHandle=probability-:吐舌头robability-of-compound-events&mode=lite" test-id="5f4558d5b6df72a2bcdbf276">

     

    In actuality, chain sandwich shops have many more types of meats, breads, cheeses, veggies, and condiments to put on your sandwich. One in particular has 16 types of meat (one of which is a no meat option), 7 types of bread, 6 types of cheese (one is a no cheese option), veggies or no veggies, and 8 types of sauces.  On top of all those options,  you can make a whole or a half sandwich.
    ::事实上,连锁三明治店拥有更多种类的肉类、面包、奶酪、蔬菜和调味品,需要放在你的三明治上。其中特别有16种肉类(其中一种是无肉选择)、7种面包、6种奶酪(其中一种是无奶酪选择)、蔬菜或无蔬菜以及8种酱。除了所有这些选择外,你可以做一个半个三明治。

    Discussion Question : Why  might it be challenging to make a tree diagram of all the  different types of sandwiches can you make ?
    ::讨论问题:为何要用树图绘制各种三明治的树图?

    As you saw in the previous interactive, you need to multiply the number of outcomes for each event to get the total number of outcomes for the compound event.  Similarly, to determine the probability of a compound event, multiply the probabilities of each event occurring together.
    ::正如您在上次互动中看到的那样, 您需要乘以每个事件的结果数量, 才能获得复合事件结果的总数。 同样, 为了确定复合事件的概率, 您需要乘以每个事件一起发生的概率 。

       Summary
    ::摘要

    • Dependent events depend on the events that happened previously; independent events do not.
      ::依附事件取决于以前发生的事件;独立事件不依附独立事件。
    • A compound event consists of two or more simple events.
      ::复合事件由两个或两个以上简单事件组成。
    • To determine the sample space for a compound event, multiply together the number of outcomes of each of the simple events.
      ::为确定复合事件的样本空间,将每个简单事件的结果数乘以一乘。