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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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Math1332Sec on7AMath1332Sec on7A
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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Math1332Sec on7AMath1332Sec on7A
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?