Section outline

  • General

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  • 可能和非同样结果之间的分辨

    In This Lesson
    ::在本课程中

    Y ou  will determine if certain experiments are fair or not. A n experiment  is an activity involving chance. Each observation (like the flip of  a coin) is a trial and each result is  an   outcome . The set of one or more outcomes is an event . The sample space is the set of all possible outcomes. For example, when flipping a coin the sample space is {heads, tails}, because those are the only possible outcomes. Notice that the { } braces are used to enclose the sample space. 
    ::您将决定某些实验是否公平。 实验是一种涉及机会的活动。 每个观察( 如硬币的翻转) 是一个试验, 每个结果都是结果。 一组一个或多个结果是一个事件。 样本空间是所有可能的结果的一组。 例如, 当翻转硬币时, 样本空间是 {头部, 尾部} , 因为这些是唯一可能的结果 。 注意 {} 括号是用来连接样本空间的 。

     

    Rolling the Dice
    ::滚骰子

    Sai and his friend Kai are rolling dice to see who gets the higher number.  They  each  roll a six-sided die and whoever gets the higher number wins the round.  If they roll the same number, then it is a tie and no one wins the round.
    ::赛亚和他的朋友凯正在玩骰子,看谁得到更高的数字。他们每人滚动六方死亡,谁得到更高的数字就赢。如果他们滚动同一数字,那么就是平局,没有人赢。

     

    INTERACTIVE
    Rolling the Dice
    minimize icon
    • Click the button to roll the two dice.

      ::单击按钮滚动两骰子。
    • Notice the changing numbers of wins!
      ::注意赢家数目的变化!
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    robability-of-independent-events" quiz-url="https://www.ck12.org/assessment/ui/embed.html?test/view/5f455e6258dba285b2de7d05&collectionHandle=probability&collectionCreatorID=3&conceptCollectionHandle=probability-:tongueoutrobability-of-independent-events&mode=lite" test-id="5f455e6258dba285b2de7d05">
    Progress
    0 / 6
    1.

    The blue numbers represent Sai's die. The green numbers represent Kai's die. The chart shows all of the possible outcomes for each roll.
    ::蓝色数字代表赛的死,绿色数字代表凯的死,图表显示每个卷的所有可能结果。

    1 2 3 4 5 6

    1

    		1.1 1,2 1,3 1,4 1,5 1,6
    2 2,1 2,2 2,3 2,4 2,5 2,6
    3 3,1 3,2 3,3 3,4 3,5 3,6
    4 4,1 4,2 4,3 4,4 4,5 4,6
    5 5,1 5,2 5,3 5,4 5,5 5,6
    6 6,1 6,2 6,3 6,4 6,5 6,6

    Select all of the following statements that are true.
    ::选择以下所有真实的语句 。

    Select all that apply
    a

    The probability Sai will win is 1 2 . It is the same for Kai.
    ::赛赢的概率是12,对凯也是一样

    b

    The probability of a tie is 6 36 = 2 12 = 1 6 .
    ::打平的概率是636=212=16。

    c

    The probability of a tie is 1 2 .
    ::领带的概率是12

    d

    The probability Sai will win is 15 36 = 5 12 . It is the same for Kai.
    ::赛赢的概率是1536=512 和凯一样

     

    Discussion Question
    ::讨论问题

    Looking at your results, is this what you expected? Are both boys equally likely to win? Why or why not? more questions about probabilities!
    ::看看你的结果,这是你所期望的吗?两个男孩都有可能赢吗?为什么不行?更多的关于概率的问题!

     

    In this experiment, the boys were both equally likely to win each trial, making it a fair experiment.  Equally likely implies that the all of the outcomes have the same probability of occurring and that the event is fair .  If something is not equally likely, then one or more outcomes are more likely to occur than others and the event would be unfair .  Think of playing a game of chance where you would have an advantage over your competitor. For example, if you were using a weighted die that always landed with six facing up, that would be unfair.
    ::在这个实验中,男孩们都同样有可能赢得每次审判,使审判成为公平的实验。同样有可能意味着所有结果都具有同样的发生概率,并且事件是公平的。如果某种情况不同样可能发生,那么一个或一个以上的结果比其他情况更有可能发生,而这种事件将是不公平的。想着玩一个赌局游戏,在那里你比竞争对手更有优势。例如,如果你使用一个总与六人对面的加权死亡,那将是不公平的。

     

    Flipping the Coin
    ::翻翻硬币

    Sai and Kai decide to flip coins now to see whose coin lands on head. If the coins land on the same side, it's a tie.  Kai is very competitive and really wants to win so he uses unfair  coins.
    ::赛和凯决定现在翻硬币,看看谁的硬币落在头上。如果硬币在同一侧着陆,那就是领带。凯非常有竞争力,非常想赢,所以他用不公平的硬币。

    • Move the red points to change the likelihood of each coin landing on heads or tails.
      ::移动红点以改变每个硬币在头部或尾部着陆的可能性。
    • The probabilities for Sai's coin are located below the table.
      ::Sai硬币的概率在桌子下方。
    • The probabilities for Kai's coin are located on the left side of the table.
      ::Kai硬币的概率位于桌子左侧。

     

    INTERACTIVE
    Flipping Unfair Coins
    minimize icon

    You are going to flip two coins (Kai's Coin and Sai's Coin) and want to know the probability of getting a specific result.

    ::你会翻两个硬币(凯的硬币和赛的硬币), 想知道获得具体结果的可能性。

    • Move the red points to change the likelihood of each coin landing on heads or tails.
      ::移动红点以改变每个硬币在头部或尾部着陆的可能性。
    • The probabilities for Sai's Coin are located below the table and the probabilities of Kai's Coin are located on the left side of the table.
      ::Sai's Coin的概率位于表下,Kai's Coin的概率位于表左侧。
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    robability-of-independent-events" quiz-url="https://www.ck12.org/assessment/ui/embed.html?test/view/5f455e7c11430dcb99167204&collectionHandle=probability&collectionCreatorID=3&conceptCollectionHandle=probability-:tongueoutrobability-of-independent-events&mode=lite" test-id="5f455e7c11430dcb99167204">

     

     Summary
    ::摘要

    • An experiment is an activity involving chance. Each observation is a trial and each result is the outcome. The set of one of more outcomes is an event. The sample space is the set of all possible outcomes.
      ::实验是一种充满机会的活动。 每种观察都是一次试验, 每种结果都是结果。 一组更多结果是一个事件。 样本空间是一组所有可能的结果 。
    • Outcomes are equally likely to occur if they have the same probability of occurring. This means that the event is fair.
      ::如果结果发生的可能性相同,结果同样可能发生,这意味着事件是公平的。
    • Outcome are not equally likely to occu r   i f one or more outcomes are more likely to occur than others. This means that  the even t is unfair.
      ::如果一种或多种结果比其他结果更有可能发生,结果就不会同样发生,这意味着该事件是不公平的。