独立活动的概率
Section outline
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Jasmine loves her funky ponytails. She has a box of 12 hair elastics and another box of 10 hair ribbons. In the box of hair elastics, there are 3 pink, 4 yellow, 2 green, and 3 purple elastics. In the ribbon box, she has 2 pink, 1 yellow, 1 green, and 6 purple ribbons. What are the chances that Jasmine will pull a purple elastic and a purple ribbon?
::茉莉花喜欢她的滑稽马尾辫。她有一盒12只发型精灵和另外一盒10条头发丝带。在发型精灵的盒子里,有3个粉红色、4个黄色、2个绿色和3个紫色长尾辫。在丝带盒里,她有2个粉红色、1个黄色、1个绿色和6个紫色丝带。茉莉花能拉一个紫色弹性带和紫色丝带的可能性有多大?In this concept, you will learn how to calculate probabilities of .
::在这一概念中,你会学会如何计算概率。Calculating Probabilities of Independent Events
::计算独立活动的概率What is the probability of two independent events both occurring? For example, what is the probability of spinner landing on red and spinner landing on blue?
::两种独立事件发生的可能性是多少?例如,在红色和蓝色的B型上浮的旋翼A着陆概率是多少?We could create a tree diagram to show all of the possible options and figure out the probability, but that is very complicated. There is a simpler way.
::我们可以创建一个树形图,显示所有可能的选项,并找出概率,但这非常复杂。有一个简单的方法。Notice that this probability equals the product of the two independent probabilities.
::请注意,这一概率等于两种独立概率的产物。
::P(红蓝色)=P(红蓝色)P(蓝色)=14/13=112The first spinner has four possible options, so the probability is . The second spinner has three possible options, so the probability is .
::第一个旋转器有四个可能的选项, 所以概率是14。 第二个旋转器有三个可能的选项, 所以概率是13。In fact, this method works for any independent events as summarized by the Probability Rule . The Probability Rule is the probability that two independent events, and , will both occur and is written as the formula:
::事实上,这种方法适用于《概率规则》概述的任何独立事件。
::P(A和B) = P(A) P(B)What is the probability that if you spin the spinner two times, it will land on yellow on the first spin and red on the second spin?
::如果你把旋转器旋转两次, 它会在第一次旋转时降落在黄色上, 在第二次旋转时降落在红色上, 概率是多少?First, define the value for each probability:
::首先,定义每个概率的值 :
::P( 黄色和红色) = P( 黄色) P( 红色) P( 红色) P( 黄色) = 35 P( 红色) = 25Next, substitute the values into the Probability Rule formula:
::其次,将数值替换为概率公式 规则公式:
::P(黄和红)=3525Then, multiply for the probability of both events occurring:
::然后,乘以两种事件的发生概率:
::P(黄和红)=3525=625The answer is the probability of both of these events occurring is .
::答案是这两起事件的发生概率是625起。Examples
::实例Example 1
::例1Earlier, you were given a problem about Jasmine and her box of ribbons and box of elastics for her funky ponytails.
::早些时候,你得到一个问题 关于茉莉花 和她的盒子 丝带 和一盒埃利亚斯特克 她的臭马尾辫。If the box of ribbons contains 2 pink, 1 yellow, 1 green, and 6 purple ribbons, and the box of elastics contains 3 pink, 4 yellow, 2 green, and 3 purple elastics, what is the probability she will pull a purple ribbon and purple elastic out of the respective boxes?
::如果丝带盒装有2个粉红色、1个黄色、1个绿色和6个紫色的丝带, 和怪兽盒装有3个粉红色、4个黄色、2个绿色和3个紫色的色带, 她能把紫色的丝带和紫色的弹性从各自的盒子里拉出来吗?First, define the value for each probability:
::首先, 定义每种概率的值 : P( 纯丝带和紫弹性) = P( 纯丝带) P( 纯弹性) = 610= 35P( 纯弹性) = 312= 14Next, 将值替换为概率规则公式 : P( 纯丝带和紫弹性) = 3514, 然后, 乘以两个事件的发生概率 : P( 纯丝带和紫弹性) = 3514= 320 。 回答是这两种事件的发生概率为 320 。Example 2
::例2The probability of rain tomorrow is 40 percent. The probability that Jeff’s car will break down tomorrow is 3 percent. What is the probability that Jeff’s car will break down in the rain tomorrow?
::明天下雨的概率是40%。 杰夫的汽车明天破损的概率是3%。 杰夫的汽车在明天的雨中破损的概率是多少? 杰夫的汽车在明天的雨中破损的概率是多少?First, define the value for each probability:
::首先,定义每个概率的值 :
::P( 断裂和断裂) = P( 断裂) P( 断裂) P( 断裂) = 4040100 = 25P( 断裂) = 33100Next, substitute the values into the Probability Rule formula:
::其次,将数值替换为概率公式 规则公式:
::P(脑和断裂)=253100Then, multiply for the probability of both events occurring:
::然后,乘以两种事件的发生概率:
::P(脑和断裂)=253100=3250The answer is the probability of both of these events occurring is .
::答案是这两起事件的发生概率是3250。Use the spinners below to answer the following questions.
::使用下面的螺旋体回答下列问题。Example 3
::例3What is the probability of spinner A landing on red and spinner B landing on red?
::旋翼A降落在红色和旋翼B着陆在红色上的可能性是多少?First, define the value for each probability:
::首先,定义每个概率的值 : P( 红色和红色) = P( red)P( red) P( red) = 14P( red) = 13Next, 将值替换为概率规则公式 : P( red) 和 red) = 14. 13 。 然后, 两次事件的概率乘以 : P( red) 和 red) = 14. 13= 112 。 答案是这两种事件的概率 112 。Example 4
::例4What is the probability of spinner A landing on blue or yellow and spinner B landing on blue?
::旋翼A降落在蓝色或黄色上的概率是多少? 旋翼B降落在蓝色上的概率是多少?First, define the value for each probability:
::首先,定义每个概率的值 : P( 蓝色或黄色或蓝色) = P( 蓝色或黄色) P( 蓝色或黄色) = 24= 12P( 蓝色) = 13Next, 将值替换为概率规则公式 : P( 蓝色或黄色和蓝色) = 12/13 后, 乘以同时发生事件的概率 : P( 蓝色或黄色和蓝色) = 1213= 16 。 答案是这两种事件的发生概率为 16 。Example 5
::例5What is the probability of spinner A landing on yellow and spinner B landing on red or green?
::旋翼A降落在黄色和旋翼B降落在红色或绿色上的概率是多少?First, define the value for each probability:
::首先, 定义每个概率的值 : P( 黄色和红色或绿色) = P( 黄色或绿色) P( 红色或绿色) =14P( 黄色) = 14P( 红色或绿色) = 23Next, 将值替换为概率规则公式: P( 黄色和红色或绿色) = 14. 23 = 212= 16 。 答案是这些事件发生的可能性是 16 。Review
::回顾Solve each problem.
::解决每一个问题。-
Mia spins the spinner two times. What is the probability that the arrow will land on 2 both times?
::米娅旋转了两次旋转器。箭头两次降落的概率是多少? -
Mia spins the spinner two times. What is the probability that the arrow will land on 2 on the first spin and 3 on the second spin?
::米娅旋转了两次旋转器。箭头在第一个旋转时投落2,第二个旋转时投落3的概率是多少? -
Mia spins the spinner two times. What is the probability that the arrow will land on an even number on the first spin and an odd number on the second spin?
::Mia 旋转旋转了两次 。 箭头在第一个旋转时投下一个偶数和第二个旋转时投下一个奇数的概率是多少 ? -
Mia spins the spinner two times. What is the probability that the arrow will land on an odd number on the first spin and a number less than 4 on the second spin?
::Mia 旋转旋转了两次 。 箭头在第一个旋转时落到一个奇数和第二个旋转时落到一个小于4的数值的概率是多少 ? -
A laundry bag has 8 black socks and 2 white socks. If you pull out a sock, then put it back in the bag and pull out a second sock, what is the probability that both socks will be black? Write your answer as a decimal.
::洗衣袋里有8个黑袜子和2个白袜子。如果你把袜子拿出来,然后把它放回袋子里,再拿出第二只袜子,两只袜子都黑的可能性有多大?把答案写成小数。 -
A laundry bag has 8 black socks and 2 white socks. If you pull out a sock, then put it back in the bag and pull out a second sock, what is the probability that both socks will be white? Write your answer as a decimal.
::洗衣袋有8个黑袜子和2个白袜子。如果你把袜子拿出来,然后把它放回袋子里,再拿出第二只袜子,两只袜子是白色的概率是多少?把回答写成小数。 -
A laundry bag has 8 black socks and 2 white socks. If you pull out a sock, then put it back in the bag and pull out a second sock, what is the probability that the first sock will be black and the second sock will be white? Write your answer as a decimal.
::洗衣袋有8个黑袜子和2个白袜子。如果你把袜子拿出来,然后放回袋子里,再放出第二只袜子,第一只袜子是黑色,第二只袜子是白色的概率有多大?把答案写成小数。 -
Dirk as a 52-card deck. The deck has 4 Aces, 4 Kings, Queens, and so on. What is the probability that Dirk will pick an Ace out of the deck? Write your answer as a simplified fraction.
::德克牌为52卡牌甲板。 甲板有 4 A、 4 K、 Queens 等。 德克从甲板上选取A的概率有多大? 将您的回答写成简化的分数 。 -
Dirk as a 52-card deck. The deck has 4 Aces, 4 Kings, Queens, and so on. What is the probability that Dirk will pick a face card (Jack, Queen, King) out of the deck? Write your answer as a simplified fraction.
::德克牌为52张牌牌牌。 甲板有4张A, 4张K, 皇后等。 德克在甲板上选一张脸牌( Jack, Queen, King) 的概率是多少? 将您的回答写成一个简化的分数 。 -
Dirk as a 52-card deck. The deck has 4 Aces, 4 Kings, Queens, and so on. Assuming that an Ace has a value of 1, what is the probability that Dirk will pick a card of lower value than a Jack out of the deck? Write your answer as a simplified fraction.
::德克牌为52张牌牌牌。 甲板有4张A, 4张K, 皇后等。 假设一个A的值为1, 德克从甲板上挑一张比杰克低价值的牌的概率是多少? 将您的回答写成一个简化的分数 。 -
Karina flips a coin 3 times. What is the probability that she will flip heads 3 times in a row?
::Karina翻了3次硬币 她一次翻3次头的概率有多大? -
Karina flips a coin 4 times. What is the probability that she will flip heads 4 times in a row?
::Karina翻了4次硬币 她一次翻4次头的概率有多大? -
Karina flips a coin 4 times. What is the probability that she will NOT flip heads 4 times in a row?
::Karina翻了4次硬币。她不会连续翻4次头的概率是多少? -
Karina flips a coin 5 times. What is the probability that she will flip heads once?
::Karina翻了5次硬币 她翻过一次头的概率有多大? -
Karina flips a coin 5 times. What is the probability that she will flip tails once?
::卡琳娜翻了5次硬币 她翻过一次尾巴的可能性有多大?
Review (Answers)
::回顾(答复)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 。 -
Mia spins the spinner two times. What is the probability that the arrow will land on 2 both times?