8.For atrip youpack 5shirts and 3pairs ofpant

# 8.For atrip youpack 5shirts and 3pairs ofpant

8.For atrip youpack 5shirts and 3pairs ofpants, and two jackets.Assumingeverything canbewornwitheverything else,howmanydif-ferentcombinations canyouwear?9.Supposeyouhave6pictures, andyouwanttoarrange4ofthemalongawall.Inhowmanydifferentwayscanyouarrange them?10.Abasketball squadhas12players.(a) Ifallplayerscanplayanyposition,howmanywayscanateamoffivebechosen?(b) Ifonlyfourplayersoutofthe12areabletobethecenter, howmanywayscanateam bechosen?11.Aboxcontains 3marbles: 1red, 1green, and 1blue. Consider anexperiment thatconsists oftaking 1marble fromthe boxand thenreplacingitintheboxanddrawingasecondmarblefromthebox.(a) Describethesamplespace.(b) Describethesamplespace,whenthesecondmarbleisdrawnwith-outreplacingthefirstmarble.12.Agameconsisting offlippingacoinendswhenthe player getstwo headsinarow,twotailsinarow,orflipsthecoinfourtimes.(a) Drawatreediagramtoshowthewaysinwhichthegamecanend.(b) Inhowmanywayscanthegameend?13.Twodicearethrown. LetEbethe eventthat the sumofthe diceisodd,letFbetheeventthat atleastoneofthedicelandson1,andletGbetheeventthat thesumis5.Describetheevents(a) E??F (b) E??F(c) F??G(d) E??F0(e)E??F??G14.Threecoinsaretossed.(a) Listtheelementsinthesamplespace.(b) Findtheprobability that exactlytwoheadsshow.15.Youflipanunfaircoin,44wherep(heads) =3 andp(tails)= 1 ,tentimes.(a) Findp(exactly 9heads). (b) Findp(exactly 7heads). (c) Findp(at least7heads).16.Atotal of500married workingcoupleswerepolledabouttheirannualsalaries,withthefollowinginformation resulting:lessthen \$25,000morethen \$25,000lessthen \$25,000212198morethen \$25,0003654Wife HusbendForinstance,in36ofthecouples,thewifeearnedmoreandthehusbandearnedlessthan\$25,000.Ifoneofthecouples israndomlychosen,whatis(a) theprobability that thehusband earnslessthan \$25,000?(b) theconditionalprobabilitythat thewifeearnsmorethan \$25,000giventhatthehusband earnsmorethan thisamount?(c)theconditionalprobability that thewifeearnsmorethan \$25,000giventhatthehusband earnslessthan thisamount?17.Iftwofairdicearerolled,what istheconditional probability that thefirstonelandson6giventhat thesumofthediceis9?18.Whatisthe probability that afaircoinlands Heads4times out of5flips?319.Ataparty, 1 oftheguestarewomen.75%percentofthewomenworesandalsand40%ofthemenworesandals. (a) Whatisthe probability that apersonchosenat random at theparty isamanwearingsandals?(b) Whatistheprobability that apersonchosenatrandomiswearingsandals?20.Amanufactureroffrontlightsforautomobilestestslampsunderahigh-humidity,high-temperatureenvironmentusingintensity andusefullifeastheresponsesofinterest. Thefollowingtableshowstheperformanceof140lamps:usefullifesatisfactoryunsatisfactorysatisfactory intensity7614unsatisfactoryintensity3218(a) Findtheprobability that arandomly selectedlampwillyieldsat-isfactoryusefullifeandsatisfactory intensity.(b) Find theprobability that arandomly selectedlamphassatisfac-toryusefullifegiventhat ithassatisfactory intensity.