Homework 1.pdfVIP免费

Homework11.(TextbookSection1.4-12)Let12,,AAbeanarbitraryinfinitesequenceofevents,andlet12,,BBbeanotherinfinitesequenceofeventsdefinedasfollows:11212312341234,,,,ccccccBABAABAAABAAAAProvethat11PrPrfor1,2,nniiiiABnAndthat11PrPriiiiAB(Hint:forthesecondpart,youneedtoprovethat11iiiiABbyshowingthateveryelementof1iiAbelongsto1iiBandeveryelementof1iiBbelongsto1iiA.)2.(Textbooksection1.6-6)Supposethatnpeopleareseatedinarandommannerinarowofntheaterseats.WhatistheprobabilitythattwoparticularpeopleMichaelandMichellewillbeseatednexttoeachother?3.(Textbooksection1.6-18)Supposethat100studentsaredividedintofiveclasses,eachcontaining20students,andthatawardsaretobegivento10ofthesestudents.Ifeachstudentisequallylikelytoreceiveanaward,whatistheprobabilitythatexactlytwostudentsineachclasswillreceiveawards?4.Apackagecontains10differentsouvenirsaboutBeijing,10differentsouvenirsaboutShanghai,10differentsouvenirsaboutXi’an,10differentsouvenirsaboutSeouland10differentsouvenirsaboutNewYork.Supposethat10souvenirsarerandomlyselectedfromthepackage.(1)WhatistheprobabilitythattheselectioncontainsnosouvenirsaboutSeoul?(2)WhatistheprobabilitythattheselectioncontainsnosouvenirsaboutBeijing,ShanghaiorXi’an?(3)Whatistheprobabilitythattheselectionmissessouvenirsaboutatleastoneplace?