GRE数学精选练习题二十

1.A,B,C,D,E,F排在1,2,3,4,5,6六个位置上,问A不在1,B不在2,C不在3的情况下,共有多少种排法?(A)720(B)450(C)180(D)216(E)3202.一直线L过点A(5,0),B(0,2),坐标原点为O,点P(X,Y)为三角形OAB中一点,问:Y(A)1/4(B)3/8(C)1/2(D)5/8(E)3/43.Inaninsurancecompany,eachpolicyhasapaperrecordandanelectricrecord.Forthosepolicieshavingincorrectpaperrecord,60%alsohavingincorrectelectricrecord;Forpolicieshavingincorrectelectricrecord,75%alsohavingincorrectpaperrecord%ofallpolicieshavebothincorrectpaperandincorrectelectricrecords.Ifwerandomlypickoutonepolicy,what’stheprobabilitythattheonehavingbothcorrectpaperandcorrectelectricrecords?(A)0(B)0(C)0(D)0(E)0.IfBobcandoajobin20daysandJanecandothejobin30days,theyworktogethertodothisjobandinthisperiod,Bobstopworkfor2daysandJanestopworkforxdays,andthejobbefinishedfor14days,whatisx?(A)1(B)3(C)1(D)1(E)1.TheprobabilityofAis60%andtheprobabilityofBis50%,whatisthemostpossibleprobabilitythatneitherAnorBwouldhappen?(A)0(B)0(C)0(D)0(E)0.Thereare1200respondentstoapoll,eachfavoringtheirpreferenceforcandidatesA,B,andC%favoredA,48%favoredB,and42%favoredC,andthereis30%favoredbothAandB.what’sthelargestpossiblenumberofrespondentsfavoringC,butnotC&B,norC&A?(A)25%(B)30%(C)28%(D)38%(E)40%参考答案：1.解：首先考虑总的可能性为，再考虑A在1，B在2，C在3的可能性分别为，中重复计算了三者交集，分别为AB在1，2，AC在1，3，BC在2，3，所需将三种情况加回，即，但考虑这三种加回的交集又重复计算了ABC在1，2，3的情况，所以应减去P332.解：在平面直角坐标系中，T3.解：设总数为x，设incorrectpaperrecord有y,incorrectelectricrecord有z，则：x·y·60%=3%·xy=5%x·z·75%=3%·xz=4%则，两者至少有一个错误的百分比为5%+4%-3%=6%，所正确答案为94%4.解：1/20(14-2)+1/30(14-x)=1，得出x=1.解：划出图表来可以一目了然：A，B均不发生的最大概率为40%，最小概率为0.解：A和B的并集为：54%+48%-30%=72%，所C为28%.