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2022年二项分布高考试题 .pdf

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1、二项分布练习题目：1.某人射击一次击中目标的概率为0.6，经过 3 次射击,此人恰有两次击中目标的概率为2.加工某种零件需经过三道工序。设第一、二、三道工序的合格率分别为109、98、87，且各道工序互不影响。(1)求该种零件的合格率；(2)从该种零件中任取3 件，求恰好取到一件合格品的概率和至少取到一件合格品的概率。（）解：98771 0981 0P；（）解法一：该种零件的合格品率为107，由独立重复试验的概率公式得：恰好取到一件合格品的概率为12373()0.1891010C，至少取到一件合格品的概率为.973.0)103(13解法二：恰好取到一件合格品的概率为12373()0.18910

2、10C，至少取到一件合格品的概率为12223333373737()()()0.9 7 3.1 01 01 01 01 0CCC3.9 粒种子分种在甲、乙、丙3 个坑内，每坑3 粒，每粒种子发芽的概率为5.0，若一个坑内至少有1 粒种子发芽，则这个坑不需要补种；若一个坑内的种子都没发芽，则这个坑需要补种。（）求甲坑不需要补种的概率；（）求 3 个坑中恰有1 个坑不需要补种的概率；（）求有坑需要补种的概率。（）解：因为甲坑内的3 粒种子都不发芽的概率为81)5.01(3，所以甲坑不需要补种的概率为.8 7 5.087811（）解：3 个坑恰有一个坑不需要补种的概率为.

3、041.0)81(87213C（）解法一：因为3 个坑都不需要补种的概率为3)87(，所以有坑需要补种的概率为.330.0)87(13解法二：3 个坑中恰有1 个坑需要补种的概率为,287.0)87(81213C恰有 2 个坑需要补种的概率为,0 4 1.087)81(223C3 个坑都需要补种的概率为.002.0)87()81(0333C4.某学生在上学路上要经过4 个路口，假设在各路口是文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3

4、G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6

5、E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3

6、G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6

7、E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3

8、G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6

9、E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3

10、G6K9 HK8X4K9G7R2 ZC6E6S4S4U3否遇到红灯是相互独立的，遇到红灯的概率都是13，遇到红灯时停留的时间都是2min.（）求这名学生在上学路上到第三个路口时首次遇到红灯的概率；（）求这名学生在上学路上因遇到红灯停留的总时间x 的分布列.（）设这名学生在上学路上到第三个路口时首次遇到红灯为事件A，因为事件 A 等于事件“这名学生在第一和第二个路口没有遇到红灯，在第三个路口遇到红灯”，所以事件 A 的概率为11141133327P A.（）由题意，可得可能取的值为0，2，4，6，8（单位：min）.事件“2k”等价于事件“该学生在路上遇到k次红灯”（k0，1，2，3，4），44

11、1220,1,2,3,433kkkPkCk，即的分布列是0 2 4 6 8 P16813281827881181文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码

12、:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9

13、G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码

14、:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9

15、G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码

16、:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9

17、G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U35.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23和12，且各株大树是否成活互不影响求移栽的4 株大树中：（）两种大树各成活1 株的概率；（）成活的株数的分布列及期望值。解：设kA表示甲种大树成活k 株，k0，

18、1，2 lB表示乙种大树成活l 株，l0，1，2 则kA，lB独立.由独立重复试验中事件发生的概率公式有文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1

19、P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2

20、 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1

21、P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2

22、 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1

23、P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2

24、 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U32221()()()33kkkkP AC,2211()()()22llllP BC.据此算得01()9P A,14()9P A,24()9P A.01()4P B,11()2P B,21()4P B.()所求概率为2111412()()()929P ABP

25、 AP B.()解法一：的所有可能值为0，1，2，3，4，且0000111(0)()()()9436PP ABP AP B,011011411(1)()()92946PP ABP AB,021120114141(2)()()()949294PPABPABPAB=1336,122141411(3)()()94923PP ABP AB.22411(4)()949PP AB.综上知有分布列0 1 2 3 4 P 1/36 1/6 13/36 1/3 1/9 从而，的期望为111311012343663639E73（株）文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文

26、档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X

27、4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文

28、档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X

29、4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文

30、档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X

31、4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文

32、档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3解法二：分布列的求法同上令12，分别表示甲乙两种树成活的株数，则12:21B(2,)，B(2,)32故有121EE241=2=，2332从而知1273EEE文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K

33、9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编

34、码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K

35、9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编

36、码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K

37、9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3文档编码:CG1P5I3G6K9 HK8X4K9G7R2 ZC6E6S4S4U3

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