1228AF12t2v3_sol.pdf

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Department
Mathematics
Course
Mathematics 1225A/B
Professor
Jennifer Mori
Semester
Winter

Description
November2012Mathematics1228ACODE333Page1Test2MakeupPARTA18marks11markAnexperimentconsistsofdrawing6ballsfromaboxwith10red5greenand15blueballsWhichoneofthefollowingsetscanbeasamplespaceforthisexperimentAatleast5ballsareblueatleastoneballisredatleastoneballisgreenBmoreredthangreenmoregreenthanredsamenumberofall3coloursCallballsareredallballsarebluesomeballsaregreenDmorebluethangreenmoregreenthanbluesamenumberofblueandgreenEnotmorethan4bluenotmorethanonerednotmorethanonegreenSolutionWeneedtoidentifywhichoneofthesetsisacompletesetofnonoverlappingdescriptionsofthethingsthatcouldhappenwhenthisexperimentisperformedTheonlysetsatisfyingboththesecriteriaisthesetmorebluethangreenmoregreenthanbluesamenumberofblueandgreenEverydrawingof6ballsmusttoneofthosedescriptionsandnodrawingcouldpossiblyttwoofthosedescriptionsatthesametimeThesetallballsareredallballsarebluesomeballsaregreenisnotcompletesincethepossibilitythatsomeredballsandsomeblueballsbutnogreenballsaredrawndoesnottanyofthedescriptionsSimilarlythesetmoreredthangreenmoregreenthanredsamenumberofall3coloursisnotcompletesincetherecouldbethesamenumberofredandgreenballsbutadierentnumberofblueballsThedescriptionsinthesetatleast5ballsareblueatleastoneballisredatleastoneballisgreenoverlapanydrawingwithbothredandgreendrawnorexactly5bluedrawntstwoofthedescriptionsLikewisethedescriptionsinthesetnotmorethan4bluenotmorethanonerednotmorethanonegreenoverlapinfacttheycouldallbetrueatthesametimeif4blue1redand1greenaredrawn21markFortheexperimentinQuestion1whichofthefollowingeventsoccurswithprobability1ANotallballsareredBAtleastoneoftheballsisblueorredCTherearemoreblueballsthanredDAtleastoneoftheballsisgreenorredENoblueandnoredballsaredrawnSolutionAneventwhichoccurswithprobability1iscertaintooccurTheonlyoneoftheanswerchoiceswhichisaneventthatiscertaintooccurisatleastoneoftheballsisblueorredSincethereareonlyredblueandgreenballsandthereareonly5greenthenanydrawingof6ballsmustincludeatleastonenotgreenballieatleastoneballwhichisblueorredcc31markIfPrE03PrF07andPrEF01ndPrEFA01B021C079D09E0ccSolutionSincePrE03thenPrE10307AndbypartitioningEthisgivesccccccccPrEPrEFPrEFPrEFPrEPrEF070106SonowpartitioningeventFwegetccPrFPrEFPrEFPrEFPrFPrEF070601cAlternativelywecouldhavepartitionedFandthenEOrwecouldndtheanswermoredirectlybycccccrealizingthatEFEFsoPrEF1PrEF10109ThisgivesPrEFPrEPrFPrEF03070901
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