1228AF12t2v2_sol.pdf

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

Description
SaturdayNovember102012Mathematics1228ACODE222Page1Test2PARTA18marks11markAnexperimentconsistsofdrawing6ballsfromaboxwith10red5greenand15blueballsWhichoneofthefollowingsetscanbeasamplespaceforthisexperimentAnotmorethan4bluenotmorethanonerednotmorethanonegreenBallballsareredallballsarebluesomeballsaregreenCmorebluethangreenmoregreenthanbluesamenumberofblueandgreenDmoreredthangreenmoregreenthanredsamenumberofall3coloursEatleast5ballsareblueatleastoneballisredatleastoneballisgreenSolutionWeneedtoidentifywhichoneofthesetsisacompletesetofnonoverlappingdescriptionsofthethingsthatcouldhappenwhenthisexperimentisperformedTheonlysetsatisfyingboththesecriteriaisthesetmorebluethangreenmoregreenthanbluesamenumberofblueandgreenEverydrawingof6ballsmusttoneofthosedescriptionsandnodrawingcouldpossiblyttwoofthosedescriptionsatthesametimeThesetallballsareredallballsarebluesomeballsaregreenisnotcompletesincethepossibilitythatsomeredballsandsomeblueballsbutnogreenballsaredrawndoesnottanyofthedescriptionsSimilarlythesetmoreredthangreenmoregreenthanredsamenumberofall3coloursisnotcompletesincetherecouldbethesamenumberofredandgreenballsbutadierentnumberofblueballsThedescriptionsinthesetatleast5ballsareblueatleastoneballisredatleastoneballisgreenoverlapanydrawingwithbothredandgreendrawnorexactly5bluedrawntstwoofthedescriptionsLikewisethedescriptionsinthesetnotmorethan4bluenotmorethanonerednotmorethanonegreenoverlapinfacttheycouldallbetrueatthesametimeif4blue1redand1greenaredrawn21markFortheexperimentinQuestion1whichofthefollowingeventsoccurswithprobability1ANoblueandnoredballsaredrawnBTherearemoreblueballsthanredCAtleastoneoftheballsisgreenorredDNotallballsareredEAtleastoneoftheballsisblueorredSolutionAneventwhichoccurswithprobability1iscertaintooccurTheonlyoneoftheanswerchoiceswhichisaneventthatiscertaintooccurisatleastoneoftheballsisblueorredSincethereareonlyredblueandgreenballsandthereareonly5greenthenanydrawingof6ballsmustincludeatleastonenotgreenballieatleastoneballwhichisblueorredcc31markIfPrE03PrF07andPrEF01ndPrEFA09B079C021D01E0ccSolutionSincePrE03thenPrE10307AndbypartitioningEthisgivesccccccccPrEPrEFPrEFPrEFPrEPrEF070106SonowpartitioningeventFwegetccPrFPrEFPrEFPrEFPrFPrEF070601cAlternativelywecouldhavepartitionedFandthenEOrwecouldndtheanswermoredirectlybycccccrealizingthatEFEFsoPrEF1PrEF10109ThisgivesPrEFPrEPrFPrEF03070901
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