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1 . 某中学参加成都市数学竞赛初赛结束后,为了解竞赛成绩情况,从所有学生中随机抽取100名学生,得到他们的成绩,将数据整理后分成五组:
,
,
,
,
,并绘制成如图所示的频率分布直方图.
的人能进决赛,入围分数应设为多少分(保留两位小数);
(2)采用分层随机抽样的方法从成绩为80~100的学生中抽取容量为6的样本,再从该样本中随机抽取3名学生进行问卷调查,求至少有1名学生成绩不低于90的概率;
(3)进入决赛的同学需要再经过考试才能参加冬令营活动.考试分为两轮,第一轮为笔试,需要考2门学科,每科笔试成绩从高到低依次有
,
,
,
,
五个等级.若两科笔试成绩均为
,则直接参加;若一科笔试成绩为
,另一科笔试成绩不低于
,则要参加第二轮面试,面试通过也将参加,否则均不能参加.现有甲、乙、丙三人报名参加,三人互不影响.甲在每科笔试中取得
,
,
,
,
的概率分别为
,
,
,
,
;乙在每科笔试中取得
,
,
,
,
的概率分别为
,
,
,
,
;丙在每科笔试中取得
,
,
,
,
的概率分别为
,
,
,
,
;甲、乙、丙在面试中通过的概率分别为
,
,
.求甲、乙、丙能同时参加冬令营的概率.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a142765f29499673b40e26ce4f1d36d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d27b00644365909601ed84ff49813d5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e19eb06f4d72f09820825ccd49c31b72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/328fcb58a789bd05648864910ede4d36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ea74afcb17a3c5f6d00f21d6e2d50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8ee628efd6b2f7296c106dd5cbae42f.png)
(2)采用分层随机抽样的方法从成绩为80~100的学生中抽取容量为6的样本,再从该样本中随机抽取3名学生进行问卷调查,求至少有1名学生成绩不低于90的概率;
(3)进入决赛的同学需要再经过考试才能参加冬令营活动.考试分为两轮,第一轮为笔试,需要考2门学科,每科笔试成绩从高到低依次有
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52fb0da8e51c0825a65db9432f80c779.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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52fb0da8e51c0825a65db9432f80c779.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52fb0da8e51c0825a65db9432f80c779.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52fb0da8e51c0825a65db9432f80c779.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f5509bf3a18d6cef73c8c43eb982ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52fb0da8e51c0825a65db9432f80c779.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)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba8930e9a26a52a6b09740c1dddbd40e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52fb0da8e51c0825a65db9432f80c779.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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d33adb74906403b0b00fcbd9fa691d8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3ffd5c35bba71ea54c28622b6cf505d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba8930e9a26a52a6b09740c1dddbd40e.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b696b79a748797ef1e56fa31ee9a450d.png)
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2023-11-03更新
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3卷引用:四川省成都市彭州市2023-2024学年高二上学期期中考试数学试题
四川省成都市彭州市2023-2024学年高二上学期期中考试数学试题四川省成都市蓉城名校联盟2023-2024学年高二上学期期中联考数学试题(已下线)10.2事件的相互独立性【第三练】“上好三节课,做好三套题“高中数学素养晋级之路
解题方法
2 . 科学家在1927年至1929年间发现自然界中的氧含有三种同位素,分别为
,
,
,根据1940年比较精确的质谱测定,自然界中这三种同位素的含量比为
占99.759%,
占0.037%,
占0.204%.现有3个
,2个
,n个
,若从中随机选取1个氧元素,这个氧元素不是
的概率为
.
(1)求n;
(2)若从中随机选取2个氧元素,求这2个氧元素是同一种同位素的概率.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a9dc664d947943da18e0010f9c2f061.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48028f9d071dd55fa5d7041872ceff32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35d43433030bcbb586ad3a9acd30c144.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a9dc664d947943da18e0010f9c2f061.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48028f9d071dd55fa5d7041872ceff32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35d43433030bcbb586ad3a9acd30c144.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a9dc664d947943da18e0010f9c2f061.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48028f9d071dd55fa5d7041872ceff32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35d43433030bcbb586ad3a9acd30c144.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48028f9d071dd55fa5d7041872ceff32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf31876698721a199c7c53c6b320aa86.png)
(1)求n;
(2)若从中随机选取2个氧元素,求这2个氧元素是同一种同位素的概率.
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2022-03-18更新
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6卷引用:四川省眉山市东坡区多悦高级中学校等2023-2024学年高二上学期期中联考数学试题
四川省眉山市东坡区多悦高级中学校等2023-2024学年高二上学期期中联考数学试题河南省新乡市2021-2022学年高三上学期期末考试数学(文科)试题(已下线)第03讲 互斥事件和独立事件-【帮课堂】2021-2022学年高一数学同步精品讲义(苏教版2019必修第二册)北师大版(2019) 必修第一册 名校名师卷 专题六 概率(已下线)12.2 古典概率(五大题型)(分层练习)-2023-2024学年高二数学同步精品课堂(沪教版2020必修第三册)(已下线)专题15.1概率-重难点突破及混淆易错规避(苏教版2019必修第二册)
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3 . 2022年北京冬奥会吉祥物“冰墩墩”,冬残奥会吉祥物“雪容融”,它们的设计充分体现了中国优秀传统文化和奥运精神的融合.如下图.某老师为了增加吉祥物“冰墩墩”和“雪容融”在班级学生中的印象,进行了拼词游戏.请同学在大小相同的6个乒乓球上分别写上“冰”、“墩”、“墩”、“雪”、“容”、“融”,再请其他同学从6个乒乓球中一次取出3个,进行拼词游戏.
![](https://img.xkw.com/dksih/QBM/2022/4/25/2965909831868416/2967006345928704/STEM/b3d6c17799974e1e8b2455ad8b349577.png?resizew=160)
(1)若某同学一次抽取三个乒乓球进行拼词游戏,求能拼成吉祥物名称的概率.
(2)若某位同学抽取的三个乒乓球中,至少抽到一个“墩”的概率.
![](https://img.xkw.com/dksih/QBM/2022/4/25/2965909831868416/2967006345928704/STEM/b3d6c17799974e1e8b2455ad8b349577.png?resizew=160)
(1)若某同学一次抽取三个乒乓球进行拼词游戏,求能拼成吉祥物名称的概率.
(2)若某位同学抽取的三个乒乓球中,至少抽到一个“墩”的概率.
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2022-04-27更新
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3卷引用:四川省凉山州西昌市2021-2022学年高二下学期期中考试数学(文)试题
解题方法
4 . 在森林草原防灭火工作中,包括甲,乙在内6名教师被分配到A,B,C,D,E五个不同的执勤点参与执勤,每个执勤点至少要有一名教师.求:
(1)甲、乙两名教师同时在A执勤点执勤的概率;
(2)甲、乙两名教师不在同一执勤点执勤的概率.
(1)甲、乙两名教师同时在A执勤点执勤的概率;
(2)甲、乙两名教师不在同一执勤点执勤的概率.
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