题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030004226-83575.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030004226-62639.png)
(1)两种大树各成活1株的概率;
(2)成活的株数
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030004226-20825.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030004226-79347.png)
(Ⅱ) 综上知
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030004226-20825.png)
![]() | 0 | 1 | 2 | 3 | 4 |
P | 1/36 | 1/6 | 13/36 | 1/3 | 1/9 |
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030004226-20825.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030004227-79931.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030004227-23179.png)
解析
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030004227-49398.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030004227-14784.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030004227-48676.png)
(I)相互独立试验同时发生的概率所以所求概率为
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030004228-47276.png)
(2)首先确定
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030004226-20825.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030004226-20825.png)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030004227-49398.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030004227-14784.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030004227-49398.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030004227-14784.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030004228-91212.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030004228-32080.png)
据此算得
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030004228-28291.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030004229-40826.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030004229-41631.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030004229-26427.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030004229-49267.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030004229-69471.png)
(Ⅰ) 所求概率为
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030004230-49854.png)
(Ⅱ) 解法一:
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030004226-20825.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030004230-45267.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030004230-83727.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030004230-24276.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030004231-11849.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030004231-77603.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030004231-67325.png)
综上知
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030004226-20825.png)
![]() | 0 | 1 | 2 | 3 | 4 |
P | 1/36 | 1/6 | 13/36 | 1/3 | 1/9 |
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030004226-20825.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030004231-24119.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030004227-23179.png)
解法二:分布列的求法同上
令
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030004231-96049.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030004232-70858.png)
故有
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030004232-17201.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030004232-91933.png)
核心考点
试题【某单位为绿化环境,移栽了甲、乙两种大树各2株.设甲、乙两种大树移栽的成活率分别为和,且各株大树是否成活互不影响.求移栽的4株大树中:(1)两种大树各成活1株的概】;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/20191030/20191030004211-94306.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030004211-65265.png)
(Ⅰ)求移栽的4株大树中恰有3株成活的概率;
(Ⅱ)设移栽的4株大树中成活的株数为
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030004211-64836.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030004211-64836.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030004202-87135.png)
(1)求
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030004202-87135.png)
(2)求1件产品的平均利润(即
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030004202-87135.png)
(3)经技术革新后,仍有四个等级的产品,但次品率降为
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030004202-51690.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030004202-80101.png)
(1)求X的分布列;
(2)求1件产品的平均利润(即X的数学期望);
(3)经技术革新后,仍有四个等级的产品,但次品率降为1%,一等品率提高为70%.如果此时要求生产1件产品获得的平均利润不小于4.73万元,则三等品率最多是多少?
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030004111-16201.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030004111-27313.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030004111-16201.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191030/20191030004111-27313.png)
![]() | 0 | 1 | 2 |
![]() | ![]() | ![]() | ![]() |
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