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Math1332Sec on7AMath1332Sec on7A

Example1

AfamilywithtwochildrenListalltheoutcomeAfamilywithtwochildrenListalltheoutcome

Solu on:Solu on:

UsingBtorepresentaboyandGtorepresentagirl,therearefourdifferentpossiblebirthorders(outcomes):BB,BG,GB,andGG

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Math1332Sec on7AMath1332Sec on7A

Example2

Applythetheore calmethodtofindtheprobabilityofthefollowing:

a.exactlyoneheadwhenyoutosstwocoins

b.ge nga3whenyourolla6-sideddie

Solu on:Solu on:

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Math1332Sec on7AMath1332Sec on7A

Example3

Thereare52playingcardsinastandarddeck.Therearefoursuits,knownashearts,spades,diamonds,andclubs.Eachsuithascardsforthenumbers2through10plusajack,queen,king,andace(foratotalof13cardsineachsuit).No cethatheartsanddiamondsarered,whilespadesandclubsareblack.Youdrawonecardatrandomfromastandarddeck.

Findthefollowingprobability

a) Aspadeisdrawn

b) AblackcardisdrawnAblackcardisdrawn

Solu on:Solu on:

PopperPopper

Problem1Problem1

Whatistheprobabilitythatfromadeckofcard,afacecardisdrawn(king,queenjack)?

a) 3/13 b) ½ c) ¼ d)Noneoftheabove

PopperPopper

Problem2Problem2

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Math1332Sec on7AMath1332Sec on7A

Whatistheprobabilitythatfromadeckofcard,aredcardisdrawn?a) 1/4 b) 1/6 c) ½ d) Noneoftheabove.1/4 b) 1/6 c) ½ d) Noneoftheabove.

Example4

Assuminganequalchanceofhavingaboyorgirlatbirth,whatistheprobabilityofhaving?

a) Allboysinafamilyoffourchildren?

b) ThreegirlsandoneboySolu on:Solu on:

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PopperPopper

Problem3Problem3

Assuminganequalchanceofhavingaboyorgirlatbirth,whatistheprobabilityofhaving2boysandtwogirlsinafamilyoffourchildren?

a) 3/8 b)1 c)8/3 d)½ e)Noneoftheabove.3/8 b)1 c)8/3 d)½ e)Noneoftheabove.

PopperPopper

Problem4Problem4

Findtheprobabilityofatleastoneheadwhenyoutosstwofaircoins.

a) 2/4

b) 1/4

c) ¾

d) 1

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Math1332Sec on7AMath1332Sec on7A

Example5

Ifyouareinterestedonlyinthenumberofheadswhentossingtwocoins,thenthepossibleeventsare0heads,1head,and2heads.Supposeyourepeatatwo-cointoss100 mesandyourresultsareasfollows:

a) 0headsoccurs22 mes.b) 1headoccurs51 mes.c) 2headsoccurs27 mes.Comparetherela vefrequencyprobabili estothetheore calprobabili es.Doyouhavereasontosuspectthatthecoinsareunfair?Comparetherela vefrequencyprobabili estothetheore calprobabili es.Doyouhavereasontosuspectthatthecoinsareunfair?

Solu on:Solu on:

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Math1332Sec on7AMath1332Sec on7A

Example6

Iden fythemethodthatresultedinthefollowingstatements.

a.Iam100%certainthatyouwillbehappywiththishouse.b.Basedongovernmentdata,thechanceofdyinginanautomobileaccidentduringaone-yearperiodisabout1in8000

c.Theprobabilityofrollinga1witha6-sideddieis=1/6

Solu on

a) Subjec veSubjec ve

b) Rela veRela ve

c) Theore calTheore cal

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Fromexample,4abovewefoundprobabilityofallboysare1/16Fromexample,4abovewefoundprobabilityofallboysare1/16

ProbabilityofNOboysallgirlsinthefamilyoffourchildrenwillbeProbabilityofNOboysallgirlsinthefamilyoffourchildrenwillbe

(1-1/16)=15/16(1-1/16)=15/16

Anotherexample:Anotherexample:

ProbabilityofraintodayinHoustonis0.4or40%ProbabilityofraintodayinHoustonis0.4or40%

ProbabilityofNOraintodayinHoustonis0.6or60%ProbabilityofNOraintodayinHoustonis0.6or60%

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Math1332Sec on7AMath1332Sec on7A

TwoDiceDistribution

Example7

Whatistheprobabilityforasumof12tooccurinrollingtwodices?Solu on:Solu on:

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Math1332Sec on7AMath1332Sec on7A

Example8

Whataretheoddsforge ngtwoheadsintossingtwofaircoins?

Solu onSolu on

Oddsforge ngtwoheadsintossingtwofaircoins

PopperPopper

Problem5Problem5

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Math1332Sec on7AMath1332Sec on7A

Findoddsagainstge ngtwotailsintossingtwofaircoins.

a) 3to1

b) 1to3

c) 4to0

d) 1to4

e) Noneoftheabove.Noneoftheabove.

Example9

Atacarrace,theoddsonBluecararegivenas7to2.Ifyoubet$10andBluecarwins,howmuchwillyougain?

Solu onSolu on

The7to2oddsmeanthat,foreach$2youbetonBluecar,yougain$7ifyouwin.A$10betisequivalenttofive$2bets,soyougain5(7)=$35

Youalsogetyour$10back,soyouwillreceive$45whenyoucollectonyourwinning cket.

Whatifyoulose?Howmuchwillyoulose?Whatifyoulose?Howmuchwillyoulose?