题目
题型:不详难度:来源:
(2)对5副不同的手套进行不放回抽取,甲先任取一只,乙再任取一只,然后甲又任取一只,最后乙再任取一只.对于下列事件:①A:甲正好取得两只配对手套;②B:乙正好取得两只配对手套.试判断事件A与B是否独立?并证明你的结论.
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108022604-14066.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108022604-68638.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108022605-17910.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108022605-66184.png)
解析
试题分析:
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108022605-25311.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108022605-92377.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108022605-71818.png)
直线3ρcosθ+4ρsinθ+a=0的普通方程为:
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108022606-93021.png)
又圆与直线相切,所以
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108022606-52331.png)
解得:
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108022604-14066.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108022604-68638.png)
(2)解:①P(A)=
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108022606-23252.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108022606-23252.png)
②
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108022606-74396.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108022606-23252.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108022606-23252.png)
∵P(AB)=
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108022606-23252.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108022606-23252.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108022605-17910.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108022607-61526.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108022605-17910.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108022605-66184.png)
点评:中档题,本题综合性较强,覆盖面较广。考查知识点注重了基础。其中(1)化为直角坐标方程,利用几何法研究直线与圆相切问题,是常见方法。相互独立事件的概率满足
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108022605-17910.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108022605-66184.png)
核心考点
试题【(1)在极坐标系中,已知圆ρ=2cosθ与直线3ρcosθ+4ρsinθ+a=0相切,求实数a的值.(2)对5副不同的手套进行不放回抽取,甲先任取一只,乙再任取】;主要考察你对极坐标与直角坐标等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108022554-61653.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108022554-38775.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108022554-61653.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108022554-59609.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108022554-70479.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108022555-25939.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108022554-61653.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108022554-70479.png)
(2) 某旅游景点给游人准备了这样一个游戏,他制作了“迷尼游戏板”:在一块倾斜放置的矩形胶合板上钉着一个形如“等腰三角形”的八行铁钉,钉子之间留有空隙作为通道,自上而下第1行2个铁钉之间有1个空隙,第2行3个铁钉之间有2个空隙,…,第8行9个铁钉之间有8个空隙(如图所示).东方庄家的游戏规则是:游人在迷尼板上方口放人一球,每玩一次(放入一球就算玩一次)先付给庄家2元.若小球到达①②③④号球槽,分别奖4元、2元、0元、-2元.(一个玻璃球的滚动方式:通过第1行的空隙向下滚动,小球碰到第二行居中的铁钉后以相等的概率滚入第2行的左空隙或右空隙.以后小球按类似方式继续往下滚动,落入第8行的某一个空隙后,最后掉入迷尼板下方的相应球槽内).恰逢周末,某同学看了一个小时,留心数了数,有80人次玩.试用你学过的知识分析,这一小时内游戏庄家是赢是赔? 通过计算,你得到什么启示?
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108022555-87681.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108022548-88011.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108022549-77989.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108022549-70906.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108022549-50726.png)
A.相离 B.相切 C.过圆心 D.相交不过圆心
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108022542-69004.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108022542-23909.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108022533-97350.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108022533-68785.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108022534-36665.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108022534-77627.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108022534-86279.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108022534-62756.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108022534-58379.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108022534-86279.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108022535-34301.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108022535-26367.png)
(1)写出曲线
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108022535-34301.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108022534-86279.png)
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108022535-15678.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108022535-96425.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108022529-75881.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191108/20191108022530-91865.png)
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