![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c6c7567972273b4ba733b47bf9d5408.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
(1)若该地区男性患者36人,请列出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b72fcdc709e77910cd36a26369648b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83caa0ad94044a1e206b1cc0b3f85080.png)
(2)某药品研发公司欲安排甲乙两个研发团队来研发此疾病的治疗药物.两个团队各至多安排2个接种周期进行试验.甲团队研发的药物每次接种后产生抗体的概率为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20c11f6c800b8e0410674a0c6d307d26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b140e221ddf537b8964fff8557cca0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ca664b1e82da6f50064a76fe118aa80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de8610232c77741a37463feba1a66c94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a20929b6b11f8c09ac0f53fe5f1cd77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72583e4cbf9e64cf692ecf600983fdee.png)
附:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e3821f70c08c5180e9b3086d3c9610f.png)
![]() | 0.10 | 0.05 | 0.01 | 0.005 | 0.001 |
![]() | 2.706 | 3.841 | 6.635 | 7.879 | 10.828 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7354d822475cfe3535b765d3d93f753a.png)
(1)为了解喜爱篮球运动是否与性别有关,某统计部门在某地随机抽取了男性和女性各100名进行调查,得到
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b72fcdc709e77910cd36a26369648b3.png)
喜爱篮球运动 | 不喜爱篮球运动 | 合计 | |
男性 | 60 | 40 | 100 |
女性 | 20 | 80 | 100 |
合计 | 80 | 120 | 200 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83caa0ad94044a1e206b1cc0b3f85080.png)
(2)某校篮球队的甲、乙、丙、丁四名球员进行传球训练,第1次由甲将球传出,每次传球时,传球者都等可能将球传给另外三个人中的任何一人,如此不停地传下去,且假定每次传球都能被接到.记甲第
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45e03e7f8bdd53063fdccec3c99f9ac2.png)
(i)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bccb0a31524b85aa2f4d4c012b04f9d8.png)
(ii)判断第24次与第25次触球者是甲的概率的大小.
附:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7dc70b5e1ba847b9918a50f67bfbe8f.png)
0.1 | 0.05 | 0.01 | 0.005 | 0.001 | |
2.706 | 3.841 | 6.635 | 7.879 | 10.828 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc799084b142019f173728370a7bc32e.png)
学生与最近食堂间的距离![]() | ![]() | ![]() | ![]() | ![]() | ![]() | 合计 |
在食堂就餐 | 0.15 | 0.10 | 0.00 | 0.50 | ||
点外卖 | 0.20 | 0.00 | 0.50 | |||
合计 | 0.20 | 0.15 | 0.00 | 1.00 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(2)根据频率分布表补全样本容量为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4abb59695562b3a1295a251dc97da700.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b72fcdc709e77910cd36a26369648b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83caa0ad94044a1e206b1cc0b3f85080.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f05ba29eb90358e2211e1f7ba6423fa2.png)
根据频率分布表列出如下的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b72fcdc709e77910cd36a26369648b3.png)
学生距最近食堂较近 | 学生距最近食堂较远 | 合计 | |
在食堂就餐 | |||
点外卖 | |||
合计 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/169d6162056f4486756c34256f5a4cd7.png)
附:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2187714e660234f0b72f2b47d3ea685a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/356b05e46b10ee51c3e43546d73ec96c.png)
![]() | 0.10 | 0.010 | 0.001 |
![]() | 2.706 | 6.635 | 10.828 |
性别 | 速度 | 合计 | |
快 | 慢 | ||
男生 | 65 | ||
女生 | 55 | ||
合计 | 110 | 200 |
(2)现有n
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e5e07bf129b073f37b553fbca100172.png)
(i)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be604061cf1591f7069472269d4c9719.png)
(ii)求证:这n根绳子恰好能围成一个圈的概率为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f34a85a61fcc926833ed2775f376541.png)
附:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5c1698cf3a31568a8ff6f6d4ee280e8.png)
0.100 | 0.050 | 0.025 | 0.010 | |
k | 2.706 | 3.841 | 5.024 | 6.635 |
不及格 | 及格 | |
师范类毕业 | 20 | 45 |
非师范类毕业 | 20 | 15 |
(2)考生甲为提升笔试成绩,报名参加了某教师资格考试知识竞赛,该竞赛要回答A,B两类问题,每位参赛者回答n次(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e443574f8ccb2467ff11a8d0a19d8b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b2a698891d42c70b597f0da4f215f09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d61cf9e5cde8a6151a06b19c4cdec33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
附:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f8ec200973736ac8bcd9aa633855d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/356b05e46b10ee51c3e43546d73ec96c.png)
0.05 | 0.025 | 0.01 | |
3.841 | 5.024 | 6.635 |
①男生所占比例为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/358d1067c81a8f997a4d457088a769d5.png)
②不喜欢体育锻炼的学生所占比例为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b267e290d2db301797edd8afef98afc7.png)
③喜欢体育锻炼的男生比喜欢体育锻炼的女生多50人.
(1)完成
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b72fcdc709e77910cd36a26369648b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83caa0ad94044a1e206b1cc0b3f85080.png)
性别 | 体育锻炼 | 合计 | |
喜欢 | 不喜欢 | ||
男 | |||
女 | |||
合计 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5f1e5d29de6e4d72bfed62d9c14dde5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1f9fabbbe61a759e52ec975215e2e7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26308ea6d8f321d27acbd7f9b131f9f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9faccaa71316eb97aaf56af15365425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccdfce3e1a14a3c03fb83779afeb6ab2.png)
(ⅱ)对于随机事件
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b2a3318f82fec39c53c0e4fea00f75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/440b506283eb35a094656087e7c9e4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccdfce3e1a14a3c03fb83779afeb6ab2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7721b52eede0a6aedbf38f33fab04df8.png)
参考公式及数据:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2187714e660234f0b72f2b47d3ea685a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/356b05e46b10ee51c3e43546d73ec96c.png)
0.10 | 0.05 | 0.010 | 0.001 | |
2.706 | 3.841 | 6.635 | 10.828 |
数学成绩良好 | 数学成绩不够良好 | |
语文成绩良好 | 12 | 10 |
语文成绩不够良好 | 8 | 5 |
(2)从该班的学生中任选一人,A表示事件“选到的学生数学成绩良好”,B表示事件“选到的学生语文成绩良好”,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02078ff7513b5680bce3e95007054fb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1e1849034ad805509f53448b44d6739.png)
(i)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06f93d49cd514d6b59ef888b057b3793.png)
(ii)利用该表中数据,给出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c4ed0c25bdca9d500e1704a97ecda80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8817b34c320a3003fac3ac6e8a78f38c.png)
附:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8d67c3ab70fc7d2f19567e0994afa20.png)
![]() | 0.050 | 0.010 | 0.001 |
k | 3.841 | 6.635 | 10.828 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b72fcdc709e77910cd36a26369648b3.png)
甲得分 | 乙得分 | 总计 | |
甲发球 | 18 | ||
乙发球 | 24 | ||
总计 | 24 | 60 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b72fcdc709e77910cd36a26369648b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe157a9c3fe004a25bf1fb79c8c0a1b.png)
(2)以上述
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b72fcdc709e77910cd36a26369648b3.png)
(ⅰ)若第1回合是甲先发球,设第
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb5c607987b73502db63f77c9799f4bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74bfab5f9cb89603b6313c971285ff3b.png)
(ⅱ)已知:若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a829fdd8ec0f3b7ede883cf2c3e53b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bb1263d800749814f7ed0bbce596704.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7dc70b5e1ba847b9918a50f67bfbe8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/356b05e46b10ee51c3e43546d73ec96c.png)
临界值表供参考:
0.15 | 0.10 | 0.05 | 0.010 | 0.001 | |
2.072 | 2.706 | 3.841 | 6.635 | 10.828 |
年龄 | 购买袋装月饼 | 购买礼盒月饼 |
50岁及以上 | 80 | 20 |
不超过50岁 | 60 | 40 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe157a9c3fe004a25bf1fb79c8c0a1b.png)
(2)假设
![](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/50c816169580d6ffc7292fd51a04fdc4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/734c3f0f17c53abdc316b2a5e2b77efa.png)
附:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bc485c58dbd6e50bfb352030f4a1c42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/356b05e46b10ee51c3e43546d73ec96c.png)
参考数据:
0.10 | 0.05 | 0.025 | 0.010 | |
2.706 | 3.841 | 5.024 | 6.635 |
10 . 某医科大学科研部门为研究退休人员是否患痴呆症与上网的关系,随机调查了市100位退休人员,统计数据如下表所示:
患痴呆症 | 不患痴呆症 | 合计 | |
上网 | 16 | 32 | 48 |
不上网 | 34 | 18 | 52 |
合计 | 50 | 50 | 100 |
(1)依据
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bdaf501302beeec9d077be02909e3bd.png)
(2)从该市退休人员中任取一位,记事件A为“此人患痴呆症”,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21778974e8491fe2a158e70b459217be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2711c7b65695a8c8dc9750f62c97f98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a7ff8a868880b6f722b23d86b7f6b90.png)
(i)证明:;
(ⅱ)利用抽样的样本数据,估计的值.
附:,其中
.
0.050 | 0.010 | 0.001 | |
3.841 | 6.635 | 10.828 |