2022年高考数学概率与统计部分知识点梳理 4.pdf

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1、comprehensive stri ctly is the guarantee, and the threeRuling strict Sanshi is to build a high-quality team of the inevitable requirement, is a comprehensive strictly pragmatic initiatives is the four overall strategic layout is an indispensable part of. strict three real connotation strict three r

2、eal is strict to self-cultivation, strict to right, exercise self-disci pline, sth to be real, do poineering work to be real, man. Be strict to self-cultivation, is to strengthe n the party spirit accomplishme nt, firm ideals and beliefs, to enhance the moral realm, the pursuit of noble sentiment, c

3、onsciousness away from the vulgar, and consciously resist unhealthy trends. Strict to right, is to persist in using the power for the people, according to the rules, according t o the system of the exercise of power, the power system was locked in a cage, any When to engage in privilege, not for per

4、sonal gains. Exercise self-discipline is to awe, hol ding a r uler, cauti ous, dilig ent in self reflection, a bide by Party discipline, do the incorruptible government. Sth to be real is to from reality of career pla nni ng and work, to make ideas, policies, pr ogrammes in line with the actual situ

5、ation, in li ne with the objective law, in line with the spirit of science, notambitious, not divorced from reality. To implement entrepreneurship, is down to earth, grab get right on the job really, the courage to assume responsibility, the courage to face the contradiction, good at problem solving

6、, strive to create a stand of practice people history of test performance. Real man to is to to the party and to the organization, to the people Relax, Ji Lvsong ambitious ideal, the comrades of the honest and faithful, honest man, honest, honest, fair and honest. Strict three real focus point in a

7、strict and a real word. strict implication of Marxist belief, communism, the Chinese characteristic socialism common ideal of serious political pur suit, is to improve the organizational life, carry out democratic centralism strictly organization principle, understand the rules, kee p the bottom lin

8、e, resist corrosion, etc. strict discipline, if you leave the strict word, it will lost faith, organizational slack, a nd ultimately lose cohesion and fighting capacity. the implication of words is every thing from the actual In t he test of practice, theory with pra ctice, seeking truth from facts,

9、 in truth a nd developing truth thought route is pragmatic, respect for the practice, pay attention to actual effect, is honest and loyalhonest and simple, earnest attitude, if leave the real word, will escape from the reality, plan to do virtua l work, bungle business, lost the final to popular opi

10、nion, losi ng the ruling foundation. T he three strict real strict, strict l ured, real word underpinning and tight combination, complement ea ch other. The three strict real strict not only adhere to the partys excelle nt tradition and style, but also absorb the outstanding traditional culture, and

11、 the partys ideological line is immanent and unified, and the partys fundamental purpose Immediately after the make against the provisi ons of the life of self-cultivation and fit in, to reflect the new situation of the party construction of the inherent laws of nat ure, embodies the w orld outlook

12、a nd methodology of organi c unity, the internal self-disci pline and external constraints of organic unity for Party members and cadres, official in general business put forward cl ear requirements, with distinct characteristics of the times. Strict three real special education, is the Party Centra

13、l Committee in the implementation of the eight , focusing on four winds to enter the new stage of the new major deployment, the first break, and g radually in-depth, ha s very strong pertinence and guidance, strengthen the style construction of the new de parture, departure, is to promote the partys

14、 construction and ref orm, development and stability of the work An important guarantee, to further consolidate the partys ruling foundation and ruling position, promote to achieve the goal of two hundred years, to achi eve the great rejuvenation of the Chinese nations dream, with great and far-reac

15、hi ng significance. At prese nt, we promote four overall strategic layout, implement, we must study hard practice strict three real , whole-heartedly seek development, forge ahea d promoting reform, firmly li of the rule of law, sedulous catch a party to build, in order to accelerate port city in in

16、teract ive fusion development, construction of the West River Basin core port city cohesion str ong positiv e energy. Second, to fully understand the lax serious harm of lax false presentation 1. Official, mainly is the ideals and beliefs shak en, the purpose of consciousness, lack of party spirit a

17、ccomplishment, discipline and rules do not speak. Specific performance for spiritual loss, ignoring the inter ests of the masses, indifferent to the sufferings of the masses, not the partys principle s, the party is not the party, in the party do not believe the party, disl oyalty to the party, a ma

18、n is not honest, sham, its ownFor delivery from is a party organization i s the concept of weak, in the heart, eyes without discipli ne, indivi duali sm, liberalism is serious, do not obey organization arrangement, the re quest for instructions, the report does not report to organizational procedure

19、s idli ng. 2, official corruption, lawlessness, reckless, a buse of power, abuse of power. In recent ye ars, the investigation of the corruption cases, can see, where corrupt officials always tried t o rent setting rent-se eking and coll usion, interest, with civilian dispute benefit, eat chinakayao

20、. Some cadres strictly normal to adapt, not used, some fantasy - this is a gust of wind, a scratch can still repeat yesterdays story Once more, some peopl e in the partys eighteen a nd edu cation practice is not convergence, dont acce pt hand, side t o write the check material, while income money. S

21、ome peopl e in a shoo in, self expansion, to forget oneself, do as one pleases, vig orously power rent-se eking, bartering, corruption and bribery. 3, the official is not, mainly is the spirit of slack, the status quo, negative coping, buck passi ng, did not dare to play, not高考复习专题之：概率与统计一、概率：随机事件A的

22、概率是频率的稳定值，反之，频率是概率的近似值. 随机事件A的概率0()1P A，其中当()1P A时称为必然事件； 当( )0P A时称为不可能事件P(A)=0；注：求随机概率的三种方法：（一）枚举法例 1 如图 1 所示， 有一电路AB是由图示的开关控制，闭合a，b，c，d，e五个开关中的任意两个开关，使电路形成通路则使电路形成通路的概率是分析：要计算使电路形成通路的概率，列举出闭合五个开关中的任意两个可能出现的结果总数，从中找出能使电路形成通路的结果数，根据概率的意义计算即可。解：闭合五个开关中的两个，可能出现的结果数有10 种，分别是ab、ac、ad、ae、bc、 bd、be、cd、ce

23、、de，其中能形成通路的有6 种，所以 p( 通路 )=106=53评注 : 枚举法是求概率的一种重要方法, 这种方法一般应用于可能出现的结果比较少的事件的概率计算. （二）树形图法例 2 小刚和小明两位同学玩一种游戏游戏规则为：两人各执“象、虎、鼠”三张牌，同时各出一张牌定胜负，其中象胜虎、虎胜鼠、鼠胜象，若两人所出牌相同，则为平局例如，小刚出象牌，小明出虎牌，则小刚胜；又如，两人同时出象牌，则两人平局如果用A、B、C分别表示小刚的象、虎、鼠三张牌，用A1、B1、C1分别表示小明的象、虎、鼠三张牌，那么一次出牌小刚胜小明的概率是多少？分析：为了清楚地看出小亮胜小刚的概率，可用树状图列出所有可

24、能出现的结果，并从中找出小刚胜小明可能出现的结果数。解：画树状图如图树状图。由树状图（树形图）或列表可知，可能出现的结果有 9 种，而且每种结果出现的可能性相同，其中小刚胜小明的结果有3 种所以 P（一次出牌小刚胜小明）=31点评 : 当一事件要涉及两个或更多的因素时，为了不重不漏地列出所有可能的结果，通过画树形图的方法来计算概率（三）列表法例 3 将图中的三张扑克牌背面朝上放在桌面上，从中随机摸出两张，并用这两张扑克牌上的数字组成一个两位数请你用画树形（状）图或列表的方法求：（1）组成的两位数是偶数的概率；（2）组成的两位数是6 的倍数精选学习资料 - - - - - - - - - 名师归

25、纳总结 - - - - - - -第 1 页，共 11 页comprehensive stri ctly is the guarantee, and the threeRuling strict Sanshi is to build a high-quality team of the inevitable requirement, is a comprehensive strictly pragmatic initiatives is the four overall strategic layout is an indispensable part of. strict three rea

26、l connotation strict three r eal is strict to self-cultivation, strict to right, exercise self-disci pline, sth to be real, do poineering work to be real, man. Be strict to self-cultivation, is to strengthe n the party spirit accomplishme nt, firm ideals and beliefs, to enhance the moral realm, the

27、pursuit of noble sentiment, consciousness away from the vulgar, and consciously resist unhealthy trends. Strict to right, is to persist in using the power for the people, according to the rules, accor ding t o the system of the exercise of power, the power system was locked in a cage, any When to en

28、gage in privilege, not for personal gains. Exercise self-discipline is to awe, hol ding a r uler, cauti ous, dilig ent in self reflection, a bide by Party discipline, do the incorruptible government. Sth to be real is to from reality of career pla nni ng and work, to make ideas, policies, pr ogramme

29、s in line with the actual situation, in li ne with the objective law, in line with the spirit of science, notambitious, not divorced from reality. To implement entrepreneurship, is down to earth, grab get right on the job really, the courage to assume responsibility, the courage to face the contradi

30、ction, good at problem solving, strive to create a stand of practice people history of test performance. Real man to is to to the party and to the organization, to the people Relax, Ji Lvsong ambitious deal, the comrades of the honest and faithful, honest man, honest, honest, fair and honest. Strict

31、 three real focus point in a strict and a real word. strict implication of Marxist belief, communism, the Chinese characteristic socialism common ideal of serious political pur suit, is to improve the organizational life, carry out democratic centralism strictly organization principle, understand th

32、e rules, kee p the bottom line, resist corrosion, etc. strict discipline, if you leave the strict word, it will lost faith, organizational slack, a nd ultimately lose cohesion and fighting capacity. the implication of words is everything from the actual In t he test of practice, theory with pra ctic

33、e, seeking truth from facts, in truth a nd developing truth thought route is pragmatic, respect for the practice, pay attention to actual effect, is honest and loyalhonest and simple, earnest attitude, if leave the real word, will escape from the reality, plan to do virtua l work, bungle business, l

34、ost the final to popular opinion, losi ng the ruling foundation. T he three strict real strict, strict l ured, real word underpinning and tight combination, complement ea ch other. The three strict real strict not only adhere to the partys excelle nt tradition and style, but also absorb the outstand

35、ing traditional culture, and the partys ideological line is immanent and unified, and the partys fundame ntal purpose Immediately after the make against the provisi ons of the life of self-cultivation and fit in, to reflect the new situation of the party construction of the inherent laws of nat ure,

36、 embodies the w orld outlook a nd methodology of organi c unity, the internal self-disci pline and external constraints of organic unity for Party members and cadres, official in general business put forward cl ear requirements, with distinct characteristics of the times. Strict three real special e

37、ducation, is the Party Central Committee in the implementation of the eight , focusing on four winds to enter the new stage of the new major deployment, the first break, and g radually in-depth, ha s very strong pertinence and guidance, strengthen the style construction of the new de parture, depart

38、ure, is to promote the partys construction and ref orm, development and stability of the work An important guarantee, to further consolidate the partys ruling foundation and ruling position, promote to achieve the goal of two hundred years, to achi eve the great rejuvenation of the Chinese nations d

39、ream, with great and far-reachi ng significance. At prese nt, we promote four overall strategic layout, implement, we must study hard practice strict three real , whole-heartedly seek development, forge ahea d promoting reform, firmly li of the rule of law, sedulous catch a party to build, in order

40、to accelerate port city in interact ive fusion development, construction of the West River Basin core port city cohesion str ong positiv e energy. Second, to fully understand the lax serious harm of lax false presentation 1. Official, mainly is the ideals and beliefs shak en, the purpose of consciou

41、sness, lack of party spirit accomplishment, discipline and rules do not speak. Specific performance for spiritual loss, ignoring the interests of the masses, indifferent to the sufferings of the masses, not the partys principle s, the party is not the party, in the party do not believe the party, di

42、sl oyalty to the party, a man is not honest, sham, its ownFor delivery from is a party organization is the concept of weak, in the heart, eyes without discipli ne, indivi duali sm, liberalism is serious, do not obey organization arrangement, the re quest for instructions, the report does not report

43、to organizational procedures idli ng. 2, official corruption, lawlessness, reckless, a buse of power, abuse of power. In recent ye ars, the investigation of the corruption cases, can see, where corrupt officials always tried to rent setting rent-se eking and coll usion, interest, with civilian dispu

44、te benefit, eat chinakayao. Some cadres strictly normal to adapt, not used, some fantasy - this is a gust of wind, a scratch can still repeat yesterdays story Once more, some peopl e in the partys eighteen and education practice is not convergence, dont acce pt hand, side t o write the check materia

45、l, while income money. Some peopl e in a shoo in, self expansion, to forget oneself, do as one pleases, vig orously power rent-se eking, bartering, corruption and bribery. 3, the official is not, mainly is the spirit of slack, the status quo, negative coping, buck passi ng, did not dare to play, not

46、的概率分析： 本题可通过列表的方法，列出所有可能组成的两位数的可能情况，然后再找出组成的两位数是偶数的可能情况和组成两位数是 6 的倍数的可能情况。解：列的表格如下： 根据表格可得两位数有：23，24，32，34，42，43所以（ 1）两位数是偶数的概率为23（ 2）两位数是6 的倍数的概率为13点评： 当一事件要涉及两个或更多的因素时，为了不重不漏地列出所有可能的结果，通过画树形图的方法来计算概率2. 等可能事件的概率（古典概率）： P(A)=nm。3、互斥事件：（A、B互斥，即事件A、B不可能同时发生）。计算公式：P(A+B)P(A)+P(B) 。4、对立事件 ：（ A、B对立，即事件A、

47、B不可能同时发生，但A、B中必然有一个发生）。计算公式是：P （A）+ P(B) ； P(A)=1 P(A) ；5、独立事件： （事件 A、B的发生相互独立，互不影响） P(A?B)P(A) ? P(B) 。提醒：（ 1）如果事件A、B独立，那么事件A与B、A与B及事件A与B也都是独立事件；（2）如果事件A、 B相互独立，那么事件A、B至少有一个不发生的概率是1P（A B） 1P(A)P(B) ；（ 3）如果事件A、 B相互独立，那么事件 A、B至少有一个发生的概率是1P（AB） 1P(A)P(B) 。6、独立事件重复试验：事件 A在 n 次独立重复试验中恰好发生了k次的概率( )(1)kkn

48、knnP kC pp( 是二项展开式(1)npp的第 k+1 项) ，其中p为在一次独立重复试验中事件A发生的概率。提醒： （ 1）探求一个事件发生的概率，关键是分清事件的性质。在求解过程中常应用等价转化思想和分解( 分类或分步 ) 转化思想处理，把所求的事件：转化为等可能事件的概率( 常常采用排列组合的知识) ；转化为若干个互斥事件中有一个发生的概率；利用对立事件的概率，转化为相互独立事件同时发生的概率；看作某一事件在n次实验中恰有k 次发生的概率，但要注意公式的使用条件。（2）事件互斥是事件独立的必要非充分条件，反之，事件对立是事件互斥的充分非必要条件；（3）概率问题的解题规范：先设事件A

49、=“, ”， B=“, ”；列式计算；作答。二、随机变量. 1. 随机试验的结构应该是不确定的. 试验如果满足下述条件：试验可以在相同的情形下重复进行；试验的所有可能结果是明确可知的，并且不止一个； 每次试验总是恰好出现这些结果中的一个，但在一次试验之前却不能肯定这次试验会出现哪一个结果。它就被称为一个随机试验. 2. 离散型随机变量：如果对于随机变量可能取的值，可以按一定次序一一列出，这样的随机变量叫做离散型随精选学习资料 - - - - - - - - - 名师归纳总结 - - - - - - -第 2 页，共 11 页comprehensive strictly is the guara

50、ntee, and the threeRuling strict Sanshi is to build a high-quality team of the inevitable requirement, is a comprehensive strictly pragmatic initiatives is the four overall strategic layout is an i ndi spensable part of. strict three real connotation strict three real is strict to self-cultivation,