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∩G
14.Threecoinsaretossed.
(a) Listtheelementsinthesamplespace.
(b) Findtheprobability that exactlytwoheadsshow.
15.Youflipanunfaircoin,
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|
wherep(heads) =3
andp(tails)= 1 ,tentimes.
(a) Findp(exactly 9heads). (b) Findp(exactly 7heads). (c) Findp(at least7heads).
16.Atotal of500married workingcoupleswerepolledabouttheirannualsalaries,withthefollowinginformation resulting:
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Wife
Husbend
Forinstance,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?
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19.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:
usefullife
| satisfactory | unsatisfactory | |
| satisfactory intensity | 76 | 14 |
| unsatisfactoryintensity | 32 | 18 |
(a) Findtheprobability that arandomly selectedlampwillyieldsat-isfactoryusefullifeandsatisfactory intensity.
(b) Find theprobability that arandomly selectedlamphassatisfac-toryusefullifegiventhat ithassatisfactory intensity.
