teoria das probabilidades 9º

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FSCLIK JËSOCK

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;% ELRK DOSRÓZOCK SLJZF RFLZOK BKSPZLJKJOIOBKBFS

• Bfsbf k kerohvobkbf hzfhk f zlgkek {vf sãl plpvikzfs ls nlhlsbf k~kz%

• Ï krzojvçbk k Nþiol Cïskz k azksf ’Kifk nkcrk fsr ‗ {vf soheoaock ’Kslzrf fsrë ikeèkbk‗%

• K Dosrózok bks Pzljkjoiobkbfs kpkzfcf oeocokigferf iohkbk k fsrfs nlhls borls bf k~kz%

• Rfzë sobl Keróeol Hlgjkzb) gkos cledfcobl plz ckqkifozl bfGïzïf) vg cïifjzf nlhkblz k bfspfzrkz l oerfzfssf bls gkrfgëroclsplz fsrk elqk ëzfk bf fsrvbls%

• Fsrf ckqkifozl fzk nlhkblz kssçbvl f fsrkqk fgpfedkbl fgbfscljzoz bf {vf alzgk sfzok gkos cleqfeoferf kplsrkz bf glbl krfz gkos dopórfsfs bf hkedkz%

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• Gïzïf {vfzok skjfz {vkerks qf~fs rfzok {vf ikeèkz blos bkbls pkzkkplsrkz clg qkerkhfg ek skçbk bf pfil gfels vg sfos bvpil frkgjïg clgl boqoboz l pzïgol bf vg nlhl sf fsrf alssfoerfzzlgpobl%

• Clilclv fsrfs pzljifgks k Pkscki $gkrfgërocl azkecîs ;1:3 –;11:/ {vf sf oerfzfsslv pfil rfgk% Pkscki clgfèlv k rzlckzclzzfsplebîecok clg Pofzzf Afzgkr $lvrzl gkrfgërocl azkecîs ;10; – ;116/ bkebl kssog ls pzogfozls pkssls pkzk l kpkzfcogferl bkRflzok bks Pzljkjoiobkbfs%

Pzla> Nlzhf Czv~


• K pzogfozk bfaoeoèãl bl clecforl bf Pzljkjoiobkbf bfqf'sf kIkpikcf f só alo bkbk fg ;882%

• Clerzkzokgferf kl {vf sfzok bf svplz fsrf cëicvil rfg jksrkerfskpiockèöfs pkzk kiïg bls nlhls {vf sfzqozkg pkzk l sfv bfspfzrkz)

plos ek ekrvzf~k iobk'sf bokzokgferf clg l kcksl%• Ek zfpzlbvèãl bf sfzfs qoqls) gvorks bks svks ckzkcrfzçsrocks eãl

sãl plssçqfos bf bfrfzgoekz ftkcrkgferf krzkqïs bl cledfcogferlbls sfvs pzlhfeorlzfs) plbfebl'sf kpfeks bfrfzgoekz k gkolz lvgfelz pzljkjoiobkbf bf bfrfzgoekbk ckzkcrfzçsrock fsrkz pzfsferf%Kcfzck bks svks bfscljfzrks Ikpikcf rfzë borl {vf

• ’L cëicvil bks pzljkjoiobkbfs eãl ï gkos bl {vf l sfesl clgvg cleqfzrobl fg eþgfzls‗%

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• K Rflzok bks Pzljkjoiobkbfs rfqf kpfzafoèlkgferls kl ilehl blssïcvils rfebl sobl Jlzfi f Ifjfshvf $sïc% TOT/ hzkebfsogpvisolekblzfs bfssfs fsrvbls f aoekigferf Mliglhkzlq $sïc% TT/{vf clesfhvov rzkesalzgkz fsrfs cledfcogferls evg zkgl bkGkrfgërock bfqobkgferf lzhkeo~kbl%

K~kz $bl ëzkjf k~'~kdz/ – kcksl) slzrf% Nlhl bf k~kz%Nlhl fg {vf k slzrf lv l k~kz bfrfzgoekg l hkedl lv

k pfzbk%$oe ’Ifiil Veoqfzski‗/%

Kifkrózol $bl ikrog kifkrlzov/ – {vf bfpfebf blkclerfcogferl oecfzrl= svnforl às cleroehîecoks bl

avrvzl% K kplsrk ï vg clerzkrl kifkrózol%$oe ’Ifiil Veoqfzski‗/%

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:% FTPFZOÎECOKS KIFKRÓZOKS FBFRFZGOEOSRKS%

• Efsrf rópocl oerfzfssk'els fsrvbkz k pzljkjoiobkbf bf cfzrlskclerfcogferls sf zfkio~kzfg fg bfrfzgoekbks ftpfzoîecoks%

• Ilhockgferf eãl skjfgls {vki l zfsvirkbl bfssks ftpfzoîecokskerfs bf ks zfkio~kzgls) plz ossl cdkgkgls'idfs Ftpfzoîecoks

Kifkrózoks%• Ftfgpils>

• ’Rozkz vgk ckzrk à slzrf bf vg jkzkidl‗ Eãl skjfgls {vf ckzrkqko skoz

• ’Ikeèkz vg bkbl‗ Eãl skjfgls {vf eþgfzl qko ckidkz

• ’Rozkz vgk jlik bf vg skcl clg jliks clilzobks‗ Eãl skjfgls kclz bk jlik {vf qko skoz

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• Plbf clecivoz'sf {vf) vgk ftpfzoîecok ï kifkrózok sf>

o/ cledfcfgls rlbls ls sfvs plssçqfos zfsvirkbls=

oo/ ckbk qf~ {vf ï fafcrvkbk eãl sf cledfcf kerfcopkbkgferf {vkibls zfsvirkbls plssçqfos qko lclzzfz=

ooo/ plbf sfz zfpfrobk fg cleboèöfs keëilhks%

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• Sf l zfsvirkbl bk ftpfzoîecok alz cledfcobl gfsgl kerfs bfsrk sfzfkio~kz fsrk cdkgk'sf Ftpfzoîecok Bfrfzgoeosrk%

• Ftfgpil>

• ’Skjfz sf vg cvjl bf hfil sf rzkesalzgk fg ëhvk k vgk

rfgpfzkrvzk bf ;0¾C‗ Eãl ï pzfcosl fspfzkz pkzk qfz plz{vfrfgls k cfzrf~k {vf l hfil pkssk kl fsrkbl iç{vobl k fsskrfgpfzkrvzk%

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3% FSPKÈL BF ZFSVIRKBLSL FSPKÈL BF ZFSVIRKBLS ï l clenverl cvnls zfsvirkbls

sãl ls {vf sf clesobfzkg plssçqfos bf sf bkz {vkebl sfsvpöf vgk ftpfzoîecok kifkrózok%

Sf ikèl vgk glfbk kl kz l fspkèl bf zfsvirkbls ï l clenverlclesrorvçbl pfils kclerfcogferls AE $Akcf Ekcoleki/ f AC$Akcf Clgvg) rkgjïg cdkgkbk Akcf Fvzl/%

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Ek ftrzkcèãl bf vgk ckzrk bf vg jkzkidl bf 20 ckzrks lfspkèl ï clesrorvçbl plz ckbk vgk bks 20 ckzrks {vf plbfgsfz ftrzkçbks%

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sorvkèãl ï gkos pzlqëqfi lv gfels pzlqëqfi% Osrl elzgkigferf {vfzbo~fz {vf sf k pzljkjoiobkbf ï gkolz dë gkos fspfzkeèk {vf fssfkclerfcogferl sf bî% Sf k pzljkjoiobkbf pkzfcf gfelz) dë gfelzfspfzkeèk {vf fssf kclerfcogferl sf bî%

• Bf alzgk oervoroqk plbfgls bo~fz {vf

pzljkjoiobkbf bf vg kclerfcogferl ï vgk gfbobk bk plssojoiobkbf bf lclzzîecok bf vg kclerfcogferl {vkebl sf zfkio~k vgk ftpfzoîecok kifkrózok%

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2% PZLJKJOIOBKBF BF VG KCLERFCOGFERL>

BFAOEOÈÃL AZF[VFECOSRK F ZFHZK BFIKPIKCF%• Clg jksf ek obfok kerfzolz) plbf fsrkjfifcfz'sf k bfaoeoèãl

fgpçzock lv azf{vfecosrk bf pzljkjoiobkbf%

K pzljkjoiobkbf bf vg bfrfzgoekbl kclerfcogferl kifkrózol ï k pfzcferkhfg bf qf~fs {vf sf fspfzk {vf fif kclerfèk) sf sf zfpfroz k ftpfzoîecok) vg hzkebf eþgfzl bf qf~fs) eks gfsgks cleboèöfs%

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• Pzljkjoiobkbf bf vg kclerfcogferl $Ifo lv Zfhzk bf Ikpikcf/

e¾ bf cksls akqlzëqfos ï l eþgfzl bf cksls fg {vf lkclerfcogferl pzfrfebobl sf plbf bkz $l {vf oerfzfssk/%

e¾ bf cksls plssçqfos ï l eþgfzl rlrki bf cksls {vf sf plbfg bkz$l {vf plbf kclerfcfz/%

plssoqfos cksls bf e akqlzkqfos cksls bf e K p

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2% PZLJKJOIOBKBF BF VG KCLERFCOGFERL>BFAOEOÈÃL AZF[VFECOSRK F ZFHZK BF

IKPIKCF%



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Ftfgpil>

Ftpfzoîecok Kifkrózok> Ikeèkz vgbkbl clg sfos akcfs%

Kclerfcogferl pzfrfebobl>Skoz vg eþgfzl gkolz {vf 2%

E¾ bf cksls akqlzëqfos>Blos $ls eþgfzls 6 f 1/

E¾ bf cksls plssçqfos>Sfos $ls eþgfzls ;= := 3= 2= 6 f 1/

Z> K pzljkjoiobkbf bf skoz e¾ gkolz{vf 2 ï %

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2% PZLJKJOIOBKBF BF VG KCLERFCOGFERL>

BFAOEOÈÃL AZF[VFECOSRK F ZFHZK BFIKPIKCF%

6% KCLERFCOGFERLS> GVORL PZLQËQFI)PLVCL PZLQËQFI) OGPLSSÇQFI) CFZRL%

• Vg kclerfcogferl bo~'sf gvorl pzlqëqfi sf k svk pzljkjoiobkbf ïhzkebf $gkos bf gfrkbf bf cksls akqlzëqfos/%

• Vg kclerfcogferl bo~'sf plvcl pzlqëqfi sf k svk pzljkjoiobkbf ïpf{vfek $gfels bf gfrkbf bf cksls akqlzëqfos/%

Ftpfzoîecok Kifkrózok> Ikeèkz vg bkbl clg sfos akcfs%

Kclerfcogferl Vg>Skoz vg eþgfzl gfelz {vf 3%

dë : cksls akqlzëqfos$gfels bf gfrkbf/

Kclerfcogferl plvcl pzlqëqfi

Kclerfcogferl Blos>Skoz vg eþgfzl gkolz {vf ;%

dë 6 cksls akqlzëqfos$gkos bf gfrkbf/

Kclerfcogferl gvorl pzlqëqfi

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6% KCLERFCOGFERLS> GVORL PZLQËQFI)PLVCL PZLQËQFI) OGPLSSÇQFI) CFZRL%

• Sf eãl ftosrf efedvg cksl akqlzëqfi à zfkio~kèãl bl kclerfcogferl)fsrf bo~'sf ogplssçqfi) plos eãl sf plbf zfkio~kz% Bk Ifo bf Ikpikcfclecivo'sf {vf k svk pzljkjoiobkbf ï ~fzl%

• Sf rlbls ls cksls plssçqfos sãl akqlzëqfos à zfkio~kèãl blkclerfcogferl fsrf bo~'sf cfzrl) plos zfkio~k'sf sfgpzf% Bk Ifo bfIkpikcf clecivo'sf {vf k svk pzljkjoiobkbf ï vg%

Ftpfzoîecok kifkrózok> Ikeèkz vg bkbl clg sfos akcfs%

Kclerfcogferl vg>

Skoz l eþgfzl :6%eãl dë cksls akqlzëqfos

Kclerfcogferl ogplssçqfi

Kclerfcogferl blos>

Skoz vg eþgfzl gfelz {vf ;0%dë sfos cksls akqlzëqfos

Kclerfcogferl cfzrl

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1% FSCKIK BF PZLJKJOIOBKBFS

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8% KCLERFCOGFERLS F[VOPZLQËQFOS

• Sf blos kclerfcogferls rîg k gfsgk pzljkjoiobkbf bf sfzfkio~kzfg bo~fg'sf f{vopzlqëqfos%

• Ftpfzoîecok kifkrózok> Ftrzkoz vgk ckzrk bf vg jkzkidl bf 20 ckzrks%

Kclerfcogferl K>Skoz vgk ckzrk bf clpks%dë bf~ cksls akqlzëqfos $bf~ckzrks bf clpks/

Kclerfcogferl J>Skoz vgk ckzrk bf fspkbks% dë bf~ cksls akqlzëqfos $bf~ckzrks bf fspkbks/

Kclerfcogferls f{vopzlqëqfos

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4% KCLERFCOGFERLS CLGPIFGFERKZFS

• Blos kclerfcogferls sãl clgpifgferkzfs sf ls cksls akqlzëqfos àzfkio~kèãl bf vg bfifs eãl sãl akqlzëqfos à zfkio~kèãl bl lvrzl fqocf qfzsk% K slgk bks svks pzljkjoiobkbfs ï ;%

• Ftpfzoîecok kifkrózok> Ftrzkoz vgk ckzrk bf vg jkzkidl bf 20 ckzrks%

Kclerfcogferl K>Skoz vgk ckzrk bf clpks%dë bf~ cksls akqlzëqfos $bf~ckzrks bf clpks/

Kclerfcogferl J>Skoz vgk ckzrk bf fspkbks) lvzlslv pkvs% dë rzoerk cksls akqlzëqfos

Kclerfcogferls clgpifgferkzfs

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teoria das probabilidades 9º

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