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1、概率知识点整理及其相关习题解析（Probabilisticknowledgepointarrangementandrelatedexercisesanalysis）1.nballsrandomlyintoN(N=n)aboxtofindtheprobabilityofeachboxhasatmostoneball(notlimitedtosetboxcapacity).Solution:puttheNballintotheNbox,eachdropisabasicevent.Thisiseasy,the
2、problemsofclassicalprobability,becauseeachballcanbeplacedinanyboxNbox,thusthetotalofN*N*N*.Putdifferently,andeachboxuptoaballatotalofN(N-1)..[N-(n-1)]onthedifferentmethod.Sothep=Nprobability(N-1).(N-n+1)/(N^n)/=N!(n!(N-n)!(N^n)).Knowledgepoint:classicalp
3、robability.Classicalprobability[equalprobabilitymodel]characteristics:Thesamplespaceofthe*1testcontainsonlyalimitednumberofelements;Inthe*2test,thelikelihoodofeachbasiceventisthesame.With2.Nproducts,includingDdefectivegoods,takenfromthisn,whichaskedexact
4、lyk(k=D)theprobabilityofdefectivegoods?Solution:intheNproductextractedn(herereferstosamplingwithoutreplacement),allweretakenmayhaveC[n][N][nN]asuperscriptsubscript,eachmethodisabasicevent,andbecausethesymmetryofthepossibilityofeachbasiceventoccurredthats
5、ame,becauseKinDdefective,alllawmayhaveC[k][D],N-Dandn-kinthepieceofauthenticpiecesfromallpossibleC[n-k][N-D],nknowbythemultiplicationprincipleinNdevice,whichjusthappenstohavecommonKdefectiveproducthasC[k][D]C[n-k][N-D],sotheprobabilityofp=C[k][D]C[n-k][N
6、-D]/C[n][N]Pointofknowledge:multiplicationprinciple,hypergeometricprobability.In3.randomintegerof1~2000inone,asktheintegerisnotdivisibleby6,andtheprobabilitycannotbedivisibleby8?Solution:ifAisanevent,thenumberthatgetscanbedivisibleby6.Bistheevent,thenumb
7、erthatgetscanbedivisibleby8,andtheprobabilityis:P(AB=P(!!)!(A,B))=1-P(A,B)[AA,A+B!AandB]andevents=1-[P(A),+P(B),-P(AB)]Becauseof333<2000/6<334,P(A)=333/2000.isobtainedBecauseof2000/8=250,P(AB)=83/2000.isobtainedThustheprobabilityofseekingisp=1-(333/2000+
8、250/2000-83/2000)=3/4.4.,15newstudentswererandomlyassignedtothreeclasses,3ofthese15freshmenwereexcellentstudents.ask1)theprobabilityofeachclassassignedtoanexcellentstudent2)theprobabilityof3excellentstudentsassignedinthesa
