1 . 众所周知,乒乓球是中国的国球,乒乓球队内部也有着很严格的竞争机制,为了参加国际大赛,种子选手甲与三位非种子选手乙、丙、丁分别进行一场内部对抗赛,按以往多次比赛的统计,甲获胜的概率分别为
,
,
,且各场比赛互不影响.
(1)若甲至少获胜两场的概率大于
,则甲入选参加国际大赛参赛名单,否则不予入选,问甲是否会入选最终的大名单?
(2)求甲获胜场次
的分布列和数学期望.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b2a698891d42c70b597f0da4f215f09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf31876698721a199c7c53c6b320aa86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
(1)若甲至少获胜两场的概率大于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4401b1421c08e525643180aef3f6dadd.png)
(2)求甲获胜场次
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
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解题方法
2 . 学校重视高三学生对数学选修课程的学习,在选修系列4中开设了
共5个专题课程,要求每个学生必须且只能选修1门课程,设
、
、
、
是高三十二班的4名学生.
(1)求恰有2个专题没有被这4名学生选择的概率;
(2)设这4名学生中选择
专题的人数为
.求
的分布列及数学期望
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84bcace6ee17523c7abfd83accea28c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
(1)求恰有2个专题没有被这4名学生选择的概率;
(2)设这4名学生中选择
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7570cbf20635cbf9d39019bdf9d73876.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b734e8f1546481e3eb4976008a045de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b734e8f1546481e3eb4976008a045de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a123f4954cc3e526fd05619f64616b7.png)
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名校
3 . 抛掷甲,乙两枚质地均匀且四面上分别标有1,2,3,4的正四面体,其底面落于桌面,记底面上所得的数字分别为x,y.记
表示
的整数部分,如:
,设
为随机变量,
.
(Ⅰ)求概率
;
(Ⅱ)求
的分布列,并求其数学期望
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/265449d2c13e0e9388d0cb682f65d6c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4e7bf9200b351a259ddfc6c0266129d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0b00abcd9305934f4858c865397a039.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e48e54f2ce3af12221046e3306aab395.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/465f9fccba6fc95d05e0d9a2bf68162e.png)
(Ⅰ)求概率
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/347c1c33d0c597d62051cf78b03320e3.png)
(Ⅱ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e48e54f2ce3af12221046e3306aab395.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf91d54a3f1f8cdf518c49ef7678993a.png)
您最近一年使用:0次
2016-12-04更新
|
316次组卷
|
2卷引用:黑龙江省大庆市大庆铁人中学2021-2022学年高二下学期期末数学试题
4 . 给出下列四个结论:
①若
组数据
的散点都在
上,则相关系数
;
②由直线
曲线
及
轴围成的图形的面积是
;
③已知随机变量
服从正态分布![](https://img.xkw.com/dksih/QBM/2015/6/15/1572122200719360/1572122206568448/STEM/8b934d84603c48279c7d8c24d66976b6.png)
则
;
④设回归直线方程为
,当变量
增加一个单位时,
平均增加2个单位.
其中正确结论的个数为
①若
![](https://img.xkw.com/dksih/QBM/2015/6/15/1572122200719360/1572122206568448/STEM/a18c9d492099453fa87b1f70529abd54.png)
![](https://img.xkw.com/dksih/QBM/2015/6/15/1572122200719360/1572122206568448/STEM/6ffb3bd0062f4c6384687e0d66a11a87.png)
![](https://img.xkw.com/dksih/QBM/2015/6/15/1572122200719360/1572122206568448/STEM/838aa6c518874b0ab63c836896638584.png)
![](https://img.xkw.com/dksih/QBM/2015/6/15/1572122200719360/1572122206568448/STEM/548bbe724a7b4976ab682ec2d2ce3520.png)
②由直线
![](https://img.xkw.com/dksih/QBM/2015/6/15/1572122200719360/1572122206568448/STEM/3ea328d9253f4769b003cc8fa9f4aad7.png)
![](https://img.xkw.com/dksih/QBM/2015/6/15/1572122200719360/1572122206568448/STEM/42aebefca9b04517af05354324b27925.png)
![](https://img.xkw.com/dksih/QBM/2015/6/15/1572122200719360/1572122206568448/STEM/33b6f90741af4f7598f0e58fcac46d1f.png)
![](https://img.xkw.com/dksih/QBM/2015/6/15/1572122200719360/1572122206568448/STEM/4e3fef24076349f196f06dd7e5cb55ee.png)
③已知随机变量
![](https://img.xkw.com/dksih/QBM/2015/6/15/1572122200719360/1572122206568448/STEM/6fd1d6bdb4284503aea59e59a0035642.png)
![](https://img.xkw.com/dksih/QBM/2015/6/15/1572122200719360/1572122206568448/STEM/8b934d84603c48279c7d8c24d66976b6.png)
![](https://img.xkw.com/dksih/QBM/2015/6/15/1572122200719360/1572122206568448/STEM/b67c7aede76547cc92897579f35ebffd.png)
![](https://img.xkw.com/dksih/QBM/2015/6/15/1572122200719360/1572122206568448/STEM/25832e9fe25149a792c04865323ae5bc.png)
④设回归直线方程为
![](https://img.xkw.com/dksih/QBM/2015/6/15/1572122200719360/1572122206568448/STEM/810af585d30c4d86bcf8547ab047e86e.png)
![](https://img.xkw.com/dksih/QBM/2015/6/15/1572122200719360/1572122206568448/STEM/33b6f90741af4f7598f0e58fcac46d1f.png)
![](https://img.xkw.com/dksih/QBM/2015/6/15/1572122200719360/1572122206568448/STEM/99eed9ca2a974aaf9a427c425217b8c3.png)
其中正确结论的个数为
A.![]() | B.![]() | C.![]() | D.![]() |
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2011·河南焦作·一模
5 . 为了比较两种肥料
对同类橘子树产量的影响(此处橘子树的产量是指每一棵橘子树的产量,单位是千克),试验人员分别从施用这两种肥料的橘子树中随机抽取了
棵,其中
棵橘子树施用了
种肥料,另
棵橘子树施用了
种肥料作为样本进行分析,其中样本橘子树产量的分组区间为
,
,
,
,
,由此得到表
和图
的所示内容,其中表
是施用
种肥料后橘子树产量的频数分布表,图
是施用
种肥料后橘子树产量的频率分布直方图.
![](https://img.xkw.com/dksih/QBM/2011/4/7/1570106546511872/1570106551934976/STEM/63e1f90a-db2a-46fd-9895-686eec1dfbc1.png?resizew=325)
![](https://img.xkw.com/dksih/QBM/2011/4/7/1570106546511872/1570106551934976/STEM/2928f341-f1ec-45ea-a8a5-3b0b7bfbf7ef.png?resizew=288)
![](https://img.xkw.com/dksih/QBM/2011/4/7/1570106546511872/1570106551934976/STEM/c437caf2-5492-4d76-8ba8-d8fb59bbda70.png?resizew=285)
(Ⅰ)完成图
和表
,其中图
是施用
种肥料后橘子树产量的频率分布直方图,表
是施用
种肥料后橘子树产量的频数分布表,并比较施用
两种肥料对橘子树产量提高的影响那种更大,理由是什么?
表2:施用
种肥料后橘子树产量的频数分布表
(Ⅱ)把施用了
种肥料的橘子树中产量不低于
千克的橘子树记为甲类橘子树,产量小于
千克的橘子树记为乙类橘子树,现采用分层抽样方法从甲、乙两类橘子树中抽取
棵进行跟踪研究,若从抽得的
棵橘子树中随机抽取
棵进行跟踪研究结果的对比,记
为这两颗橘子树中甲类橘子树的个数,求
的分布列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90dd550e1ad9bbf01687ffb4aab788ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0efba7147f5b9ced8bc4a72f0a9fb8af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0efba7147f5b9ced8bc4a72f0a9fb8af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67c620ae3417443fea2d729f9c26861e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c64cd583c538f89bb8ad7ac2b2e136a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1518f7303c68bd06a664df4716346765.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49af36dc835291b83cf8b5dcc394a01a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e60387030a865e31ae81d19074ed61f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://img.xkw.com/dksih/QBM/2011/4/7/1570106546511872/1570106551934976/STEM/63e1f90a-db2a-46fd-9895-686eec1dfbc1.png?resizew=325)
![](https://img.xkw.com/dksih/QBM/2011/4/7/1570106546511872/1570106551934976/STEM/2928f341-f1ec-45ea-a8a5-3b0b7bfbf7ef.png?resizew=288)
![](https://img.xkw.com/dksih/QBM/2011/4/7/1570106546511872/1570106551934976/STEM/c437caf2-5492-4d76-8ba8-d8fb59bbda70.png?resizew=285)
(Ⅰ)完成图
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
表2:施用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
橘子树产量的分组 | |||||
频数 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5021dda43ea360fb7b1102c1a462693a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b184c94e38f1e5dbe750b2168c2a37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
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名校
解题方法
6 . 一厂家向用户提供的一箱产品共10件,其中有1件次品. 用户先对产品进行随机抽检以决定是否接受. 抽检规则如下:至多抽检3次,每次抽检一件产品(抽检后不放回),只要检验到次品就停止继续抽检,并拒收这箱产品;若3次都没有检验到次品,则接受这箱产品,按上述规则,该用户抽检次数的数学期望是___________ .
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10-11高二下·黑龙江·期中
解题方法
7 . 某电视节目中有一游戏,由参与者掷骰子决定向前行进格数.若掷出奇数则参与者向前走一格,若掷出偶数,则参与者向前蹦两格(跃过中间的一格),能走到终点者获胜,中间掉入陷阱者失败.已知开始位置记作第1格,终点位置为第8格,只有第7格是一个陷阱.
(I)求参与者能到第3格的概率.
(Ⅱ)求参与者掷3次骰子后,所在格数的分布列.
(III)求参与者能获胜的概率.
(I)求参与者能到第3格的概率.
(Ⅱ)求参与者掷3次骰子后,所在格数的分布列.
(III)求参与者能获胜的概率.
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8 . “开门大吉”是某电视台推出的游戏节目.选手面对1~8号8扇大门,依次按响门上的门铃,门铃会播放一段音乐(将一首经典流行歌曲以单音色旋律的方式演绎),选手需正确回答出这首歌的名字,方可获得该扇门对应的家庭梦想基金.在一次场外调查中,发现参赛选手多数分为两个年龄段:20~30;30~40(单位:岁),其猜对歌曲名称与否的人数如图所示.
(1)写出2×2列联表;判断是否有90%的把握认为猜对歌曲名称与否和年龄有关;说明你的理由;(下面的临界值表供参考)
现计划在这次场外调查中按年龄段选取9名选手,并抽取3名幸运选手,求3名幸运选手中在20~30岁之间的人数的分布列和数学期望.
![](https://img.xkw.com/dksih/QBM/2015/6/15/1572122200719360/1572122206756864/STEM/f6e06b39ce7247559fe9e0262c380182.png)
(参考公式:
其中
)
(1)写出2×2列联表;判断是否有90%的把握认为猜对歌曲名称与否和年龄有关;说明你的理由;(下面的临界值表供参考)
![]() | 0.10 | 0.05 | 0.010 | 0.005 |
![]() | 2.706 | 3.841 | 6.635 | 7.879 |
![](https://img.xkw.com/dksih/QBM/2015/6/15/1572122200719360/1572122206756864/STEM/f6e06b39ce7247559fe9e0262c380182.png)
(参考公式:
![](https://img.xkw.com/dksih/QBM/2015/6/15/1572122200719360/1572122206756864/STEM/6a45854b26c44f18a06b27b72a39eac0.png)
![](https://img.xkw.com/dksih/QBM/2015/6/15/1572122200719360/1572122206756864/STEM/3df6bdbad8fd4ce4be7660a6ad328bc6.png)
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2016-12-03更新
|
345次组卷
|
3卷引用:2015届黑龙江省哈尔滨九中高三第三次高考模拟理科数学试卷
12-13高三上·黑龙江大庆·开学考试
9 . 从装有2只红球,2只白球和1只黑球的袋中逐一取球,已知每只球被抽取的可能性相同.
(Ⅰ)若抽取后又放回,抽取3次,求恰好抽到2次为红球的概率;
(Ⅱ)若抽取后不放回,设抽完红球所需的次数为
,求
的分布列及期望.
(Ⅰ)若抽取后又放回,抽取3次,求恰好抽到2次为红球的概率;
(Ⅱ)若抽取后不放回,设抽完红球所需的次数为
![](https://img.xkw.com/dksih/QBM/2011/11/9/1570346426777600/1570346432118784/STEM/6ec163d67fc44576a9d1615c1dc6eb95.png)
![](https://img.xkw.com/dksih/QBM/2011/11/9/1570346426777600/1570346432118784/STEM/6ec163d67fc44576a9d1615c1dc6eb95.png)
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解题方法
10 . 在某单位的职工食堂中,食堂每天以
元/个的价格从面包店购进面包,然后以
元/个的价格出售.如果当天卖不完,剩下的面包以
元/个的价格全部卖给饲料加工厂.根据以往统计资料,得到食堂每天面包需求量的频率分布直方图如下图所示.食堂某天购进了80个面包,以
(单位:个,
)表示面包的需求量,
(单位:元)表示利润.
![](https://img.xkw.com/dksih/QBM/2017/3/31/1655585435525120/1657017500819456/STEM/2e2e24d2964e42ccbc5d611bf389951b.png?resizew=337)
(1)求
关于
的函数解析式;
(2)根据直方图估计利润
不少于
元的概率;
(3)在直方图的需求量分组中,以各组的区间中点值代表该组的各个值,并以需求量落入该区间的频率作为需求量取该区间中点值的概率(例如:若需求量
,则取
,且
的概率等于需求量落入
的频率),求
的分布列和数学期望.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91e07104b699c4012be2d26160976a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f15f0f1c059df25b912ae6525b311255.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://img.xkw.com/dksih/QBM/2017/3/31/1655585435525120/1657017500819456/STEM/2e2e24d2964e42ccbc5d611bf389951b.png?resizew=337)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)根据直方图估计利润
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0efba7147f5b9ced8bc4a72f0a9fb8af.png)
(3)在直方图的需求量分组中,以各组的区间中点值代表该组的各个值,并以需求量落入该区间的频率作为需求量取该区间中点值的概率(例如:若需求量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d26e3d198d14775f664b7acb6828a80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e8d180d4174157aa3f79fdf6cb60baa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e8d180d4174157aa3f79fdf6cb60baa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d27b00644365909601ed84ff49813d5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
您最近一年使用:0次
2017-04-02更新
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639次组卷
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4卷引用:【全国百强校】黑龙江省哈尔滨市第六中学2018-2019学年高二上学期期末考试数学(理)试题