uarantee for the great struggle. This aspects XI General Secretary of speech main including exercise thrift, against extravagance mass line is party of lifeline and fundamental work route accurate grasp party of mass line education practice activities of guideline and target requirements set and develop \ct three real\o system of cage in using history wisdom advance anti-corruption construction in-depth advance style clean government and anti-corruption struggle develop nail nail of spirit, a Zhang good of blueprint worked to... 9. other aspects. 18 big yilai, XI General Secretary also respectively on diplomatic, and military, and ecological construction, aspects published has important speech, covers has construction ecological civilization, and advance defense and army modern, and rich \country, two systems\ce and advance country unified, and go peace development road, and promoted building new powers relationship, and go good around diplomatic work, and strengthening and developing countries solidarity cooperation, and active participation multilateral affairs, and science of thinking and work method, many aspects. XI Jinping, Secretary of a series of important speeches, and further enrich and develop the party's theory, line, principles and policies, the party puts forward new requirements for more contemporary features, the latest achievement of Marxism in China, is a guide to persisting and developing socialism with Chinese characteristics. Four methods. To address the relationship between comprehensive and focused on science. In the process of learning, we should follow as a good study and carry out the \n\hensive collaborative learning; and with their own jobs, focus research and understanding spirit, grasp the potential requirements. For example, every party member should be according to the various branches of learning program, an article does not go into a link, no leakage of conducting a comprehensive study, and combined with their own duties and responsibilities, be focused and targeted Geoscience. Like, leaders to highlight learning XI on ruling acting political know of deep love of cut dry in practice go in forefront of river new language out poverty XI on coordination advance \l\pts XI on full deepening reform discusses excerpts XI on full law ruling discusses excerpts 18 big yilai XI on major economic problem discusses excerpts, discipline to highlight learning XI on strict party of discipline and rules discusses excerpts XI Jinping, on the construction of clean and honest Government and fight against corruption discussed excerpts, technology to highlight the learning of the XI Jinping on technological innovation and discusses excerpts, XI Jinping, education should highlight the important excerpts of work on education and so on. To address the relation between stage and often science. Phase has the advantage of time to focus on fast, to highlight the theme, focused, result; often learn the advantages of flexible fit, form, subtle, continues to第一章 概率论的基本概念
基础训练I
一、选择题
1. 以A表示事件“甲种产品畅销，乙种产品滞销”，则其对立事件A为：（ D ）。 A）甲种产品滞销，乙种产品畅销； B）甲乙产品均畅销；
C）甲种产品滞销； D）甲产品滞销或乙种产品畅销. 2、设A,B,C是三个事件，则A?B?C表示（ C ）。 A） A,B,C都发生； B） A,B,C都不发生； C） A,B,C至少有一个发生； D） A,B,C不多于一个发生 3、对于任意事件A,B，有P(A?B)?（ C ）。
A）P(A)?P(B)； B）P(A)?P(B)?P(AB)； C）P(A)?P(AB)； D）P(A)?P(B)?P(AB)。
4、已知5个人进行不放回抽签测试，袋中5道试题（3道易题，2道难题），问第3个人抽中易题的概率是( A ) 。
A） 3/5； B）3/4； C）2/4； D）3/10. 5、抛一枚硬币，反复掷4次，则恰有3次出现正面的概率是（ D ）。 A） 1/16 B） 1/8 C） 1/10 D） 1/4
6、设P(A)?0.8，P(B)?0.7，P(A|B)?0.8，则下列结论正确的有（ A ）。 A）A,B相互独立； B）A,B互不相容；
C）B?A； D）P(A?B)?P(A)?P(B)。
二、填空题
B都不发生，C发生”1.设A,B,C是随机事件，则事件“A、表示为ABC, “A,B,C至少有两个发生”表示成AB?AC?BC 。
2.设A、B互不相容，P(A)?0.4，P(A?B)?0.7，则P(B)? 0.3 ；
3. 某市有50%住户订日报，有65%住户订晚报，有85%的住户至少订这两种报纸中的一种，则同时订这两种的住户百分比是：30%；
4.设P(A)?P(B)?P(C)?1/4,P(AB)?P(BC)?0,P(AC)?1/8，则A、B、C三件事至少有一个发生的概率为：5/8；
eepen. In General, periodic high priority on learning, easy to grasp and practice: recurrent learning factors, long time, prone to \ning programmes are explicitly required to learn education is not an event, but to highlight the normal education, differentiated levels, heart, catch a fine practice, the real party's ideological and political construction in the everyday, often. This requires that we do a good job phase focused learning based on knowledge contests, comments on rewards in the form, pay special attention to recurring studies. o handle the relationship between solid strong to learn and a lot to learn. For any unit or individual, objectively speaking, in the process of carrying out the party Constitution Party rules and spirit, there is a problem with strong and weak, which we need to pay attention to the actual learning content, and handle the relationship between solid strong to learn and a lot to learn. On one hand, we must always keep a humble attitude, good deal, Continue the hardening. The other hand, always keep the spirit of energetic, pegged to the weak link to find gaps, fill the short Board. Short Board issues should not be underestimated, the saying goes, have short Board, add a short. This tells us, there are weaknesses shortcomings and do not be afraid, fear is a blind eye and not to repair, the result is poor is worse and the weak weaker. United States politics home zhamusi, and Wilson and prevention crime learn experts qiaozhikailin proposed has a famous of broken window theory, that, if a building House has a fan window of glass broken has, and this fan Windows no get timely repair, others on May to broke more of window glass, time a long, these damaged of window on to people caused a disorder, and matter of feel, results in this mass errors think no attention, and no management of atmosphere Xia, some bad culture, and violations behavior on will breeding and spread. Reality life in the is such, clean of wall Shang, suddenly was posted has a Zhang ad, if didn't people management, not out days this wall Shang on will appeared greatly small many of advertising; private take mess built phenomenon is so, began circle a small block to built a small shed put things, if didn't people timely stop, he on dare built a hut live people, time long has didn't people tube, wants to tube Shi on difficult has. Therefore, the solid strong is important, a lot to learn is also important. Third, key, grasp the learning objective of education is to train a qualified party member \on to its core essence is learning and doing. Learning and doing are mutually reinforcing, if optical can't do, study leave, real learning deficiency, while sweating, wind and water, \not the mules\ng party rules did not comply with the party Constitution, address the learning series is not used, instead, learn and do, imagine this \do you meet the eligibility requirements of party members. Therefore, the \c learning, the key is in use, do, line. In particular, is a qualified party members to grasp the following three points. To strengthen %uarantee for the great struggle. This aspects XI General Secretary of speech main including exercise thrift, against extravagance mass line is party of lifeline and fundamental work route accurate grasp party of mass line education practice activities of guideline and target requirements set and develop \ct three real\o system of cage in using history wisdom advance anti-corruption construction in-depth advance style clean government and anti-corruption struggle develop nail nail of spirit, a Zhang good of blueprint worked to... 9. other aspects. 18 big yilai, XI General Secretary also respectively on diplomatic, and military, and ecological construction, aspects published has important speech, covers has construction ecological civilization, and advance defense and army modern, and rich \country, two systems\ce and advance country unified, and go peace development road, and promoted building new powers relationship, and go good around diplomatic work, and strengthening and developing countries solidarity cooperation, and active participation multilateral affairs, and science of thinking and work method, many aspects. XI Jinping, Secretary of a series of important speeches, and further enrich and develop the party's theory, line, principles and policies, the party puts forward new requirements for more contemporary features, the latest achievement of Marxism in China, is a guide to persisting and developing socialism with Chinese characteristics. Four methods. To address the relationship between comprehensive and focused on science. In the process of learning, we should follow as a good study and carry out the \n\hensive collaborative learning; and with their own jobs, focus research and understanding spirit, grasp the potential requirements. For example, every party member should be according to the various branches of learning program, an article does not go into a link, no leakage of conducting a comprehensive study, and combined with their own duties and responsibilities, be focused and targeted Geoscience. Like, leaders to highlight learning XI on ruling acting political know of deep love of cut dry in practice go in forefront of river new language out poverty XI on coordination advance \ strategy layout discusses excerpts XI on full deepening reform discusses excerpts XI on full law ruling discusses excerpts 18 big yilai XI on major economic problem discusses excerpts, discipline to highlight learning XI on strict party of discipline and rules discusses excerpts XI Jinping, on the construction of clean and honest Government and fight against corruption discussed excerpts, technology to highlight the learning of the XI Jinping on technological innovation and discusses excerpts, XI Jinping, education should highlight the important excerpts of work on education and so on. To address the relation between stage and often science. Phase has the advantage of time to focus on fast, to highlight the theme, focused, result; often learn the advantages of flexible fit, form, subtle, continues to5. 若A、B互不相容,且P(A)?0,则P(B/A)? 0 ；若A、B相互独立，,且P(A)?0,则P(B/A)?P(B) 。
6、已知P(B)?1/3,P(BA)?1/4，P(AB)?1/6，则P(AB)= 1 / 18 。
三、计算题
1．从一批产品中取出一个产品进行检验（每次取出的产品不放回），以Ai表示“第i次取到的是合格品”，试用Ai表示(i?1,2,3)下列事件：
1）三次都取到合格品； 2）三次中至少有一次取合格品； 3）三次中恰有两次取到合格品； 4）三次中至少有两次取到合格品； 5）三次中一次也未取到合格品； 6）三次中至多有一次取到合格品； 解： 1）A1A2A3；2）A1?A2?A3；3）A1A2A3?A1A2A3?A1A2A3；
4）A1A2A3?A1A2A3?A1A2A3?A1A2A3?A1A2?A1A3?A2A3； 5）A1?A2?A3?A1?A2?A3?A1A2A3；6）A1A2?A1A3?A2A3 2．设P(A)?1/3，P(B)?1/2。在下列三种情况下求P(BA)的值：
1）AB??； 2）A?B； 3）P(AB)?1/8。 解：因 P(BA)?P(B)?P(AB)
1) P(BA)?1/2；2）P(BA)?P(B)?P(A)?1/6；3）P(BA)?3/8。
3.假设某地区位于甲、乙两河流的汇合处，当任一河流泛滥时，该地区即遭受水灾。设某
时期内甲河流泛滥的概率为0.1；乙河流泛滥的概率为0.2；当甲河流泛滥时，乙河流泛滥的概率为0.3，试求：（1）该时期内这个地区遭受水灾的概率；（2）当乙河流泛滥时,甲河流泛滥的概率。
解：设A={甲河流泛滥}，B={乙河流泛滥}，
由题意，该地区遭受水灾可表示为A?B，于是所求概率为： (1) P(A?B)?P(A)?P(B)?P(AB)?P(A)?P(B)?P(A)P(B/A) ?0.1?0.2?0.1?0.3?0.27 (2)P(A/B)?P(AB)P(A)P(B/A)0.1?0.3???0.15
P(B)P(B)0.24．有甲、乙、丙三门火炮同时独立地向某目标射击，命中率分别为0.2、0.3、0.5,求： 1）至少有一门火炮命中目标的概率；2）恰有一门火炮命中目标的概率。
解：设A、B、C分别表示甲、乙、丙火炮命中目标，则
1）P(A?B?C)?1?P(ABC)?1?P(A)P(B)P(C)?1?0.8?0.7?0.5?0.72 2）P(ABCABCABC) ?P(ABC)?P(ABC)?P(ABC)
?P(A)P(B)P(C)?P(A)P(B)P(C)?P(A)P(B)P(C) ?0.47
5、有三个形状相同的箱子,在第一个箱中有两个正品,一个次品;在第二个箱中有三个正品,一个次品;在第三个箱中有两个正品,两个次品.现从任何一个箱子中,任取一件产品,求取到
eepen. In General, periodic high priority on learning, easy to grasp and practice: recurrent learning factors, long time, prone to %uggish\ning programmes are explicitly required to learn education is not an event, but to highlight the normal education, differentiated levels, heart, catch a fine practice, the real party's ideological and political construction in the everyday, often. This requires that we do a good job phase focused learning based on knowledge contests, comments on rewards in the form, pay special attention to recurring studies. o handle the relationship between solid strong to learn and a lot to learn. For any unit or individual, objectively speaking, in the process of carrying out the party Constitution Party rules and spirit, there is a problem with strong and weak, which we need to pay attention to the actual learning content, and handle the relationship between solid strong to learn and a lot to learn. On one hand, we must always keep a humble attitude, good deal, Continue the hardening. The other hand, always keep the spirit of energetic, pegged to the weak link to find gaps, fill the short Board. Short Board issues should not be underestimated, the saying goes, have short Board, add a short. This tells us, there are weaknesses shortcomings and do not be afraid, fear is a blind eye and not to repair, the result is poor is worse and the weak weaker. United States politics home zhamusi, and Wilson and prevention crime learn experts qiaozhikailin proposed has a famous of broken window theory, that, if a building House has a fan window of glass broken has, and this fan Windows no get timely repair, others on May to broke more of window glass, time a long, these damaged of window on to people caused a disorder, and matter of feel, results in this mass errors think no attention, and no management of atmosphere Xia, some bad culture, and violations behavior on will breeding and spread. Reality life in the is such, clean of wall Shang, suddenly was posted has a Zhang ad, if didn't people management, not out days this wall Shang on will appeared greatly small many of advertising; private take mess built phenomenon is so, began circle a small block to built a small shed put things, if didn't people timely stop, he on dare built a hut live people, time long has didn't people tube, wants to tube Shi on difficult has. Therefore, the solid strong is important, a lot to learn is also important. Third, key, grasp the learning objective of education is to train a qualified party member \on to its core essence is learning and doing. Learning and doing are mutually reinforcing, if optical can't do, study leave, real learning deficiency, while sweating, wind and water, \not the mules\ng party rules did not comply with the party Constitution, address the learning series is not used, instead, learn and do, imagine this \do you meet the eligibility requirements of party members. Therefore, the \c learning, the key is in use, do, line. In particular, is a qualified party members to grasp the following three points. To strengthen %uarantee for the great struggle. This aspects XI General Secretary of speech main including exercise thrift, against extravagance mass line is party of lifeline and fundamental work route accurate grasp party of mass line education practice activities of guideline and target requirements set and develop \ct three real\o system of cage in using history wisdom advance anti-corruption construction in-depth advance style clean government and anti-corruption struggle develop nail nail of spirit, a Zhang good of blueprint worked to... 9. other aspects. 18 big yilai, XI General Secretary also respectively on diplomatic, and military, and ecological construction, aspects published has important speech, covers has construction ecological civilization, and advance defense and army modern, and rich \country, two systems\ce and advance country unified, and go peace development road, and promoted building new powers relationship, and go good around diplomatic work, and strengthening and developing countries solidarity cooperation, and active participation multilateral affairs, and science of thinking and work method, many aspects. XI Jinping, Secretary of a series of important speeches, and further enrich and develop the party's theory, line, principles and policies, the party puts forward new requirements for more contemporary features, the latest achievement of Marxism in China, is a guide to persisting and developing socialism with Chinese characteristics. Four methods. To address the relationship between comprehensive and focused on science. In the process of learning, we should follow as a good study and carry out the \n\hensive collaborative learning; and with their own jobs, focus research and understanding spirit, grasp the potential requirements. For example, every party member should be according to the various branches of learning program, an article does not go into a link, no leakage of conducting a comprehensive study, and combined with their own duties and responsibilities, be focused and targeted Geoscience. Like, leaders to highlight learning XI on ruling acting political know of deep love of cut dry in practice go in forefront of river new language out poverty XI on coordination advance \l\pts XI on full deepening reform discusses excerpts XI on full law ruling discusses excerpts 18 big yilai XI on major economic problem discusses excerpts, discipline to highlight learning XI on strict party of discipline and rules discusses excerpts XI Jinping, on the construction of clean and honest Government and fight against corruption discussed excerpts, technology to highlight the learning of the XI Jinping on technological innovation and discusses excerpts, XI Jinping, education should highlight the important excerpts of work on education and so on. To address the relation between stage and often science. Phase has the advantage of time to focus on fast, to highlight the theme, focused, result; often learn the advantages of flexible fit, form, subtle, continues to正品的概率。
解: 设Bi={从第i个箱子中取到产品}(i=1,2,3)，A={取得正品}。
由题意知Ω=B1+B2+B3 ，B1,B2,B3是两两互不相容的事件。
P(B1)=P(B2)=P(B3)=1/3， P(A|B1)=2/3, P(A|B2)=3/4, P(A|B3)=2/4=1/2 由全概率公式得 P(A)=P(B1)P(A|B1)+P(B2)P(A|B2)+P(B3)P(A|B3)=0.64 (或23/36).
6．已知商场某产品由三个厂家提供，产品次品率分别为0.02、0.01、0.03，销售份额分别占0.15、0.80、0.05，现消费者因为产品问题提出索赔，但由于保存不善标志缺失，如果你是商场负责人，想将这笔索赔转嫁给厂家，如何分摊最合理？
解：设A表示产品为不合格品,Bi(i?1,2,3)表示产品是由第i个厂家提供的, 由题可得:
p(B1)?0.15，p(B2)?0.80，p(B3)?0.05，
p(AB1)?0.02，p(AB2)?0.01，p(AB3)?0.03
由全概率公式：p(A)?p(AB1)p(B1)?p(AB2)p(B2)?p(AB3)p(B3)?0.0125
由贝叶斯公式: p(B1A)?p(AB1)p(B1)p(A)?0.02?0.15?0.240.0125；
p(B2A)?0.64；
p(B3A)?0.12.
0.64：0.12，即 6：16：3. 由上可见，比较合理的分配比例应为：0.24：基础训练Ⅱ
一、选择题
1．事件A?B又可表示为（ C ）
A）A?B B）A?AB C）A?B D）A?AB 2．设P(AB)?0,则有（ D ）
A) A和B互不相容； B) A和B相互独立；
C) P(A)?0或P(B)?0； D) P(A?B)?P(A)。 3．设A和B互为对立事件，则下列不正确的结论为( B )
A)P?B/A??0； B)A和B独立； C)P(A/B)?1； D)P(A?B)?1。
4、设事件A,B是两个概率不为零的互不相容事件，则下列结论正确的是（ D ） A）A,B互不相容； B）A与B相容； C）P(AB)?P(A)P(B)； D）P(A?B)?P(A)。
5.某人射击时，中靶的概率为3/4，如果射击直到中靶为止，则射击次数为3的概率为
( C )
eepen. In General, periodic high priority on learning, easy to grasp and practice: recurrent learning factors, long time, prone to \ning programmes are explicitly required to learn education is not an event, but to highlight the normal education, differentiated levels, heart, catch a fine practice, the real party's ideological and political construction in the everyday, often. This requires that we do a good job phase focused learning based on knowledge contests, comments on rewards in the form, pay special attention to recurring studies. o handle the relationship between solid strong to learn and a lot to learn. For any unit or individual, objectively speaking, in the process of carrying out the party Constitution Party rules and spirit, there is a problem with strong and weak, which we need to pay attention to the actual learning content, and handle the relationship between solid strong to learn and a lot to learn. On one hand, we must always keep a humble attitude, good deal, Continue the hardening. The other hand, always keep the spirit of energetic, pegged to the weak link to find gaps, fill the short Board. Short Board issues should not be underestimated, the saying goes, have short Board, add a short. This tells us, there are weaknesses shortcomings and do not be afraid, fear is a blind eye and not to repair, the result is poor is worse and the weak weaker. United States politics home zhamusi, and Wilson and prevention crime learn experts qiaozhikailin proposed has a famous of broken window theory, that, if a building House has a fan window of glass broken has, and this fan Windows no get timely repair, others on May to broke more of window glass, time a long, these damaged of window on to people caused a disorder, and matter of feel, results in this mass errors think no attention, and no management of atmosphere Xia, some bad culture, and violations behavior on will breeding and spread. Reality life in the is such, clean of wall Shang, suddenly was posted has a Zhang ad, if didn't people management, not out days this wall Shang on will appeared greatly small many of advertising; private take mess built phenomenon is so, began circle a small block to built a small shed put things, if didn't people timely stop, he on dare built a hut live people, time long has didn't people tube, wants to tube Shi on difficult has. Therefore, the solid strong is important, a lot to learn is also important. Third, key, grasp the learning objective of education is to train a qualified party member \on to its core essence is learning and doing. Learning and doing are mutually reinforcing, if optical can't do, study leave, real learning deficiency, while sweating, wind and water, \not the mules\ng party rules did not comply with the party Constitution, address the learning series is not used, instead, learn and do, imagine this \do you meet the eligibility requirements of party members. Therefore, the \c learning, the key is in use, do, line. In particular, is a qualified party members to grasp the following three points. To strengthen \