题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030005317-82437.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030005317-87352.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030005317-25895.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030005317-26254.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030005318-22357.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030005318-76075.png)
(1)若向量
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030005318-96594.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030005318-92684.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030005319-87507.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030005319-76136.png)
(2) 记点
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030005319-82041.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030005319-82041.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030005319-46801.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030005319-26098.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030005320-90017.png)
求使事件
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030005320-51238.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030005320-45970.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030005320-61307.png)
解:(1) 设向量
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030005321-66654.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030005321-65887.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030005321-72831.png)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030005321-72831.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030005321-13812.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030005321-66654.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030005321-65887.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030005322-27442.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030005322-50320.png)
显然
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030005321-66654.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030005321-65887.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030005322-94177.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030005322-48374.png)
分别从集合
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030005317-25895.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030005317-26254.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030005318-22357.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030005318-76075.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030005323-87740.png)
所以向量
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030005321-66654.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030005321-65887.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030005320-61307.png)
(2)由(Ⅰ)知;当
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030005323-41922.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030005323-75715.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030005323-39880.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030005323-99364.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030005324-13368.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030005324-22318.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030005324-86716.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030005324-29263.png)
所以使事件
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030005320-51238.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030005320-45970.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030005325-38572.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030005325-99073.png)
解析
核心考点
试题【设集合,,分别从集合和中随机取一个数和.(1)若向量,,求向量与的夹角为锐角的概率;(2) 记点,则点落在直线上为事件,求使事件的概率最大的. 】;主要考察你对离散型随机变量均值与方差等知识点的理解。[详细]
举一反三
(1)若从袋子中一次取出3个球,求得4分的概率;
(2)若从袋子中每次摸出一个球,看清颜色后放回,连续摸2次,求所得分数的分布列及数学期望。
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030005241-34997.png)
(1)求
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030005242-75893.png)
(2)求
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030005241-34997.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030005228-90799.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030005228-32575.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030005229-99725.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030005229-52879.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030005229-99010.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030005229-55447.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030005229-87461.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030005229-87461.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030005230-98195.png)
3 5 3 3 8 5 5 6 3 4
6 3 4 7 5 3 4 8 5 3
8 3 4 3 4 4 7 5 6 7
该行业规定产品的等级系数
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030005230-25730.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030005230-88078.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030005230-49141.png)
(1)试分别估计该厂生产的产品的一等品率、二等品率和三等品率;
(2)从样本的一等品中随机抽取2件,求所抽得2件产品等级系数都是8的概率
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030005153-53039.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030005153-32115.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030005153-25789.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030005154-27043.png)
(Ⅰ)若三辆汽车中恰有一辆汽车被堵的概率为
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030005154-43907.png)
(Ⅱ)在(Ⅰ)的条件下,求三辆汽车中被堵车辆的个数
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030005154-81771.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030005146-90007.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030005146-90007.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030005146-29002.jpg)
(I)如果甲、乙来自A小区,丙、丁来自B小区,求这4人中恰有2人是低碳族的概率;
(II)A小区经过大力宣传,每周非低碳族中有20%的人加入到低碳族的行列.如果2周后随机地从A小区中任选25人,记
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030005146-31859.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030005146-31859.png)
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