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)  EF (b)  EF(c)  FG(d)  EF0

(e)EFG

 

14.Threecoinsaretossed.


 

 

(a)  Listtheelementsinthesamplespace.

(b)  Findtheprobability  that  exactlytwoheadsshow.

 

15.Youflipanunfaircoin,


 

4

 

4

 
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:

 


 

 

 

 

 

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.

 

  • Posted: 6 years ago
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