题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030002001-99366.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030002002-65549.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030002002-40514.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030002002-47553.png)
(Ⅰ)记取出的3个球颜色全不相同的概率为
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030002002-33868.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030002002-33868.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030002001-99366.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030002002-65549.png)
(Ⅱ)当
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030002003-78481.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030002003-91333.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030002003-47773.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030002003-47480.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030002004-89511.png)
解析
(1)根据题目中的条件表示概率值,结合均值不等式得到最值。
(2)先求解随机变量的各个取值的概率值,然后结合分布列而后数学期望值公式得到结论。解:(Ⅰ)由题意知
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030002004-99046.png)
当且仅当
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030002004-52392.png)
所以,当
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030002002-33868.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030002003-47480.png)
(Ⅱ)当
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030002003-78481.png)
而
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030002004-95977.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030002005-95230.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030002005-31649.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030002005-42345.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030002005-53311.png)
所以,红球个数
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030002004-95977.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030002006-30391.png)
于是
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030002006-29981.png)
核心考点
试题【甲箱中放有个红球与个白球(,且),乙箱中放有2个红球、1个白球与1个黑球。从甲箱中任取2个球,从乙箱中任取1个球。(Ⅰ)记取出的3个球颜色全不相同的概率为,求当】;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
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030001953-35841.png)
(1)从
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030001954-70103.png)
(2)在B小区中随机选择20户,从中抽取的3户中“非低碳族”数量为X,求X的分布列和期望EX.
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030001938-58392.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030001938-58893.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030001938-10050.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030001939-86495.png)