# 226 Math

8.For  atrip  youpack  5shirts  and  3pairs  ofpants,  and  two  jackets.

Assumingeverything  canbewornwitheverything  else,howmanydif-ferentcombinations  canyouwear?

9.Supposeyouhave6pictures,  andyouwanttoarrange4ofthemalongawall.Inhowmanydifferentwayscanyouarrange  them?

(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.

(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.

15.Youflipanunfaircoin,

 4
 4

andp(tails)=  1 ,tentimes.

 lessthen  \$25,000 morethen  \$25,000 lessthen  \$25,000 212 198 morethen  \$25,000 36 54

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?

 3

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.

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