Сборник задач по высшей математике 2 том

6.3.43.B «CJIOBape pyccKoro H3bIKa» C.II. 0JKeroBa 900 CTpaHl-lII;. KaKo-

Ba BepOHTHOCTb Toro, qTO Hayra,n: OTKpbITM CTpaHllu;a 6y,neT llMeTb

nopH,nKoBblil: HOMep, KpaTHblil: 13?

6.3.44.B rpynne 10 IOHoilieil: II 10 ,neBYilieK. AnH ,ne:lKypcTBa Ha Beqepe ny-

TeM :lKepe6beBKII BbI,neJIHIOT 5 qeJIOBeK. KaKoBa BepoHTHoCTb Toro, qTO B qllCJIO ,ne:lKypHbIX BOil:,nyT:

6.3.45.B ypHe 3 6eJIbIX, 6 qepHbIX II 5 CllHllX IIIapOB. 1I3 Hee BbIHllMaIOT

Hay,naqy 2 IIIapa. KaKoBa BepOHTHOCTb Toro, qTO OHII OKa:lKYTCH pa3Horo U;BeTa?

6.3.46. KaKoBa BepOHTHOCTb TOro, qTO ,nBa onpe,neJIeHHbIX cTy,neHTa 6y,nyT nOCJIaHbI Ha npaKTllKy B ropo,n C, eCJIll B HaJIllqlle llMeeTCH 5 MeCT B ropo,n A, 8 - B ropo,n B B ropo,n C?

6.3.47.10 H6JIOK, 3 rpyilill II 8 JIllMOHOB paCKJIa,n:bIBaIOT Hay,naqy B Tpll

naKeTa C paBHbIM KOJIllqeCTBOM <PPYKTOB. Hail:Tll BepOHTHOCTII co6bITllil::

6.3.48. 1I3 KOJIO,nbI B 36 KapT BbIHllMaIOT Hay,naqy 4 KapTbI. Hail:Tll BepoHTHOCTII C06bITllil:: A = {Bce KapTbI - ,naMbI}, B = {,nBe KapTbI 113 qeTblpex - IIIecTepKll}. PeilillTb 3a,n:aqy ,nJIH cxeMbI BbI6opa:

6.3.49.Ha nJIOCKOCTII Hap"coBaHbI ,nBe KOHu;eHTp"qeCK"e OKPY:lKHOCTll,

pa,n:llYCbI KOTOPbIX 3 CM II 5 CM. KaKOBa BepOHTHOCTb Toro, qTO TOqKa, 6pOIIIeHHM Hay,naqy B 60JIbilillil: Kpyr, nona,neT B KOJIbU;O, 06pa30BaHHOe 3TllMII OKPY:lKHOCTHMll?

6.3.56. KaKoBa BepOHTHOCTb TOro, qTO npOll3Be,neHlle ,nByX Hayra,n B3HTbIX npaBllJIbHbIX nOJIO:lKllTeJIbHbIX ,npo6eil: 6y,neT He 60JIbille ~?

6.3.51. .II:Ba qeJIOBeKa ,noroBOp"JI"Cb 0 BCTpeqe B onpe,neJIeHHOM MeCTe B npOMe:lKYTKe BpeMeHII OT 19.00,no 20.00. Ka:lK,nblil: 113 HllX npllxo,nllT Hay,naqy, He3aBllCllMO OT ,npyroro II O:lKll,naeT 15 MllHyT. KaKOBa BepOHTHOCTb Toro, qTO OHII BCTpeTHTcH?

6.3.52. Hay,naqy BbI611paIOT ,nBa qllCJIa 113 npOMe:lKYTKa [0,1]. KaKOBa BePOHTHOCTb Toro, qTO llX cyMMa 3aKJIIOqeHa Me:lK,ny ~ II I?

6.3.53.Ha napKeT, COCTaBJIeHHblil: 113 npaBllJIbHbIX TpeyrOJIbHllKOB co CTo-

POHOil: a, CJIyqail:Ho na,n:aeT MOHeTa pa,n:llyca r. Hail:Tll BepOHTHOCTb Toro, qTO MOHeTa u;eJIllKOM OKa:lKeTCH BHyTpli o,nHoro 113 TpeyrOJIbHllKOB.

6.3.54. CTep:lKeHb ,nJIllHbI L JIOMaIOT Ha Tpll qacTll, BbI611PM CJIyqail:HbIM 06pa30M MeCTa pa3JIOMa. Hail:Tll BepoHTHoCTb Toro, qTO 113 nOJIyqeHHbIX oTpe3KoB MO:lKHO COCTaBllTb TpeyrOJIbHllK.

300

6.3.55.3aaa"l,a-wym7Ca.

Ha )l;He rJIy6oKoro cocy)l;a

JIe:>KaT cnoKoiiHO n IIIapOB,

IIooqepe)l;Ho HX OTTY)l;a

TacKalOT )l;BOe )l;ypaKOB.

CHe 3aHHTbe HM npHHTHO,

OHH TaCKalOT m MHHyT

11, B3HBIIIH IIIap, ero o6paTHo B cocy)l; HeMe)l;JIeHHO KJIa)l;yT.

BBH)l;y YCJIOBHH TaKoro

CKOJIb BepOHTHOCTb BeJIHKa,

"(ITo nepBblii 6bIJI rJIyneii BToporo, Kor)l;a IIIapOB OH BbIHYJI k?

B.II. CKHTOBHq, 1946 r.

KOHTponbHble BonpOCbl III 60nee cnQ)KHble 3aAaHIIIR

6.3.56.12 npe)l;MeTOB npOH3BOJIbHO paccTaBJIHIOT no TpeM KOMHaTaM. Ka-

KOBa BepOHTHOCTb Toro, qTO B nepBoii KOMHaTe OKa:>KeTCH 2 npe)l;- MeTa, BO BTOpoii - 3, a B TpeTbeii - 7?

6.3.57. 113 MHO:>KeCTBa qHCeJI {I, 2, 3, ... , n} HaY)l;aqy BbI6HpalOTcH )l;Ba qHCJIa. KaKOBa BepOHTHOCTb Toro, qTO BTopoe qHCJIO 60JIbIIIe nepBO- m, eCJIH BbI60p ocy:w;eCTBJIHeTCH C B03Bpa:w;eHHeM?

6.3.58.n IIIapoB npOH3BOJIbHO paCKJIa)l;bIBaIOTCH no n rHe3)l;aM. KaKOBa

301

'iTOO,Il;HOMY H3 napOXO,Il;OB npH,Il;eTCH O:>KH,Il;aTb OCB060:>K,Il;eHHH npH-

'iaJIa,eCJIH BpeMH CTOHHKH nepBOrO napOXO,Il;a - 1 'iac,a BTOporo - 2 'iaca.

6.3.66.3aoa"l,a B'IOrj)(pO'Ita. lIrJIa )l;JIHHbI l 6pocaeTcH Ha nJIOCKOCTb, pa3-

rpaq)JIeHHYIO napaJIJIeJIbHbIMH npHMbIMH Ha nOJIOCbI IIIHPHHOit L.

Bce nOJIO:>KeHHH lI,eHTpa HrJIbI H Bce ee HanpaaJIeHHH O,Il;HHaKOBO BepOHTHbI. HaitTH BepoHTHoCTb Toro, 'iTOHrJIa nepeCe'ieTKaKYIOHH6y,Il;b npHMylO.

6.3.67. Ha OKPY:>KHOCTb pa)l;Hyca R HaY,Il;a'iYnOCTaBJIeHbI TpH TO'iKHA, B

H C. HaitTH BepOHTHOCTb TOro, 'iTOTpeyrOJIbHHK ABC - OCTpO-

yrOJIbHblit.

6.3.68. KaKoit TOJIIlI,HHbI ,Il;OJI)KHa 6bITb MOHeTa pa)l;Hyca R, 'iT06bIBepo-

HTHOCTb na)l;eHHH Ha pe6po 6bIJIa paBHa l?

T06ycOB 30 MHHyT. nernexo,Il; B CJIY'iaitHblitMOMeHT BpeMeHH OTnpaBJIHeTCH H3 A B B. KaKOBa BepOHTHOCTb Toro, 'iTOero B nyTH ,Il;OroHHT aBT06yc?

§ 4. YC110BHAH BEPOHTHOCTb

npaBIII110 YMHO>KeHIIISI BepoSiTHocTeiii

~ IIycTb A H B - HeKOTopble C06bITHH, rrpH'IeMPCB) > O. YCJlo6'1wiL 6epOSlm- 'H.Ocm'b'lO co6'btmUS! A rrpH YCJIOBHH B (0603Ha'laeTCHpeA I B)) Ha3b1BaeTCH BepoHTHOCTbIO C06b1THH A, Hait,n;eHHaH rrpH YCJIOBHH, 'ITOC06b1THe B rrpOH30IIlJIO. 2ha BepOHTHOCTb Haxo,n;HTCH rro <popMYJIe

P(AB) peA IB) = PCB) .

AHaJIOrH'IHOorrpe,n;eJIHeTCH YCJIOBHaH BepOHTHOCTb C06bITHH B rrpH YCJIOBHH A:

TeopeMa 6.3 (npaBlIIllo YMHO>KeHIIIJI BepOJlTHOcTeiii). BepoilTHoCTb npOIA3Be~e­

HlAiI ~ByX C06blTlAK paBHa npOlll3BeAeHlllIO BepOJlTHOCTIil OAHoro 1113 HIIIX Ha YCIlOBHy'1O

BepOJlTHOCTb APyroro nplll YCIlOBIIIIII, 'ITOnepBoe Co6blTlile npOIll30WIlO:

P(AB) = peA) . PCB I A) 11111111 P(AB) = PCB) . peA I B).

IIoHHTHe YCJIOBHOit BepOHTHOCTH, TaK )Ke KaK H npaeHJIO YMHO)KeHHH Bepo-

HTHocTeit eCTeCTBeHHblM 06pa30M 0606IIIaIOTCH Ha CJIY'Iait rrpOH3BOJIbHOrO '1HCJIa

302

C06bITHit. A HMeHHO, B CJIy'laen C06b1THit HMeeM

He3aBI.1CI.1Mbie C06bITI.1S1

~Co6'btmue A 't1.a3'bt6aemeJ! one3a6UCUM'btM om co6'btm'U.fl, B, eCJIH BepOHTHOCTb

C06bITHH A He 3aBHCHT OT Toro, ocyw;ecTBHJIOCb HJIH HeT C06b1THe B. ~

B 9TOM CJIy'laeYCJIOBHaH BepOHTHOCTb C06b1THH A npH YCJIOBHH B paBHa 6e3yCJIOBHOit BepOHTHOCTH C06bITHH A, T. e. BbinOJIHHeTCH paBeHCTBO

P(A IB) = P(A).

ECJIH Co6bITHe A He 3aBHCHT OT C06b1THH B, TO H Co6bITHe B He 3aBHCHT OT A. 06a C06b1THH npH 9TOM Ha3bIBaIOTCH He3aBHCHMbIMH.

TaKHM 06pa30M ,D;Ba C06bITHH Ha3b1BaIOTCH one3a6UCUM'btMU, eCJIH rrOHBJIeHHe O,D;HOrO H3 HHX He MeHHeT BepOHTHOCTH rrOHBJIeHHH ,D;pyroro.

,Il;.rrH He3aBHCHMbIX C06b1THit rrpaBHJIO YMHO:lKeHHH BepOHTHocTeit rrpHHHMaeT

BH,D;:

P(AB) = P(A) . P(B).

OTa <popMYJIa 'IaCTOHCrrOJIb3yeTcH B Ka'leCTBeorrpe,D;eJIeHHH He3aBHCHMbIX co6b1THit.

~ C06bITHH A l , A2, ... , An Ha3b1BaIOTCH one3a6UCUM'btMU (u'!/'u one3a6UCUM'btMU 6

C060'ICynonocmu), eCJIH BepOHTHOCTb Ka:lK,D;OrO H3 HHX He 3aBHCHT OT ocyw;eCTBJIeHHH

He3aBHCHMble C06b1THH A l , A 2, ... , An HBJIHIOTCH rrorrapHO-He3aBHCHMbIMH. 06paTHoe, Boo6w;e rOBopH, HeBepHO.

BepOSITHOCTb CYMMbl COBMeCTHblX C06blTI.1lii

TeopeMa 6.4. Bep01lTHOCTb CYMMbl .QBYX COBMeCTHblX C06blTHVI eCTb cyMMa IIIX

BepO"THOCTeiil MIIIHyC BepO"THOCTb IIIX n pOlll3BeAeH III". T. e.

P(A + B) = P(A) + P(B) - P(AB).

,Il;.rrH Tpex C06l>ITHit A, B H C HMeeM:

P(A + B + C) = P(A) + P(B) + P(C) - P(AB) - P(AC) - P(BC) + P(ABC).

303

B cJIY'Iae TpeX H 60JIbmerO '1HCJIa C06blTHit ~JUI HaXOlK~eHHH BepOHTHOCTH CYMMbI S 3THX C06b1THit rrpOm;e HaitTH BepOHTHOCTb rrpOTHBOrrOJIOlKHoro C06blTHH

S, a 3aTeM BOCrrOJIb30BaTbCH paBeHCTBOM P(S) = 1 - P(S).

6.4.1.BpoIIIeHbI ,II;Be IIrpaJIbHble KOCTIi. HaiiTIi BepO.HTHOCTb TOro, qTO

COCTOIiT 113 10 aJIeMeHTapHbIX C06bITlIii:

B = {(I, 1), (1, 2), (2, 1), (1,3), (3, 1), (1,4), (4, 1), (2,2), (2,3), (3, 2)}.

Co6bITlie A, onpe,II;eJI.HeMOe YCJIOBlieM B (:::lTO 3Haq1lT, qTO IICXO,II;bI, 6JIaronpll-

.HTCTBYIOIII:lIe C06bITliIO A, oT6I1paIOTC.H cpe,II;1I IICXO,II;OB, COCTaBJI.HIOIII:IIX C06bITile B), COCTOIiT 113 Tpex aJIeMeHTapHbIX IICXO,II;OB onbITa: (2,1), (2,2), (2,3).

P(A IB) = 3 lloaToMY IICKOMM BepO.HTHOCTb paBHa 10.

2.llpocTpaHcTBo aJIeMeHTapHblx C06bITlIii COCTOIiT 113 36 aJIeMeHTOB: n =

={(I, 1), (1,2), ... , (6, 6)}. ,Il;JI.H BblqllCJIeHII.H BepO.HTHOCTIi P(A I B) BOC-

6.4.2.11:3 CTaH,II;apTHOro Ha6opa,II;OMIiHO (28 IIITYK) 6epeTC.H HaY,II;aqy O,II;Ha KOCTb. KaKOBa BepO.HTHOCTb Toro, qTO aTa KOCTb 6Y,II;eT )l;y6JIeM

(T.e. 6Y,II;eT IIMeTb BII,II; 1-1, 4-411 T.,II;.), eCJIII1I3BeCTHO, qTO CYMMa OqKOB Ha Heii - qeTHOe qllCJIo?

6.4.3.HaiiTIi BepO.HTHOCTb Toro, qTO npll 6pocaHlili Tpex IIrpaJIbHbix KOcTeii XOT.H 6bI Ha o,II;Hoii Bbllla,II;eT 5 OqKOB, npll yCJIOBIIII, qTO Ha Bcex KOCT.HX BblllaJIli rpaHIi C HeqeTHbIM qllCJIOM OqKOB? C qeTHbIM qllCJIOM OqKOB?

6.4.4.BepO.HTHOCTb nOna,II;aHII.H B u:eJIb pasHa 0,3, a BepO.HTHOCTb ee YHIIqTO)l{eHII.H paBHa 0,05. HaiiTIi BepO.HTHOCTb TOro, qTO npll nona,II;a- Hlill B u:eJIb OHa 6Y,II;eT YHlIqTO)l{eHa.

304

CJIe,IJ;OBaTeJIbHO, C06bITliH K II C, K II q, C II q He3aBIiCIiMbI. TeM He MeHee, C06bITliH K, C II q He HBJIHIOTCH He3aBliCliMbIMli B cOBoKynHoCTIi. ,n:eiiCTBIITeJIbHO, P(K . C . q) = ~, a P(K) . P(C) . P(q) = ~ . ~ . ~ = ~, T.e.

A2 He3aBlic1iMbIMII? cOBMecTHbIMII?

305

. ocyrn:eCTBHTCH H C06bITHe Al , H C06bITHe A2, T. e. A = Al . A2.

a) C06bITHH Al H A2 3aBHCHMbI, T. K. HacTYIIJIeHHe C06bITHH Al BJIHHeT

6.4.14.113 KOJIO.n;bI B 36 KapT Hay.n;aqy BblHHMalOTCH TpH KapTbI (6e3 B03-

BpaTa). KaKoBa BepOHTHOCTb Toro, qTO cpe.n;H HHX He 6y.n;eT HH o.n;Hoil IIIecTepKH?

6.4.15. Cpe.n;H 100 JIoTepeilHblx 6HJIeTOB eCTb 10 BbmrpbIIIIHbIX. KaKoBa BepoHTHoCTb Toro, qTO 2 Hay.n;aqy BbI6paHHblx 6HJIeTa OK~yTCH

BbmrpbIIIIHbIMH?

6.4.16. TOJIbKO O.n;HH H3 9 KJIlOqeil IIO.n;XO.n;HT K .n;aHHOMY 3aMKy. KaKOBa BepOHTHOCTb TOro, qTO rrpH.n;eTCH orrp060BaTb 5 KJIlOqeil .n;JIH OTKpbIBaHHH 3aMKa?

6.4.17. Pa.n;HCT TPH)K.n;bI BbI3bIBaeT KoppecrroH.n;eHTa. BepoHTHoCTb Toro, qTO 6y.n;eT IIpHHHT IIepBblil BbI30B, paBHa 0,3, BTOpoil - 0,4-, TpeTHil - 0,5. 110 YCJIOBHHM IIpHeMa C06bITHH, COCTOHrn:He B TOM, qTO

.n;aHHblil BbI30B 6y.n;eT YCJIblIIIaH, He3aBHCHMbI. RailTH BepOHTHOCTb Toro, qTO KoppeCIIOH.n;eHT Bo06rn:e YCJIbIIIIHT BbI30B.

6.4.18. B Hrn:HKe co.n;ep)KaTCH 9 6eJIbIX, 6 qepHbIX H 5 3eJIeHbIX IIIapOB. Ray.n;aqy BbIHHMaeTCH O.n;HH IIIap. RailTH BepOHTHOCTb Toro, qTO OH OK~eTCH JIH60 qepHbIM, JIH60 3eJIeHbIM.

306

o IIycTb C06bITHe A = {H3BJIeqeHHblil IIIap OKroKeTCH qepHbIM}, B = {H3BJIeqeHHblil IIIap OKroKeTCH 3eJIeHbIM}. Tor.n;a C06bITHe C = {H3BJIeqeHHblil wap OKroKeTCH JIH60 qepHbIM, JIH60 3eJIeHbIM} npe.n;CTaBJIHeT c060il CyMMy

BepOHTHOCTb H3BJIeqeHHH qepHOrO HJIH 3eJIeHOrO IIIapa MO:lKHO 6bIJIO 6bI Hail-

Til 6e3 HCnOJIb30BaHHH TeopeMbI CJIO:lKeHHH BepOHTHOCTeil; Be.n;b HMeeTCH 11 paBHOB03MO:lKHbIX, 6JIarOnpHHTHbIX C06bITHlO C HCXO.n;OB: P(C) = ~~.) •

6.4.19. ,il;Ba CTpeJIKa .n;eJIalOT no O.n;HOMY BbICTpeJIY B MHIIIeHb. BepoHTHOCTb nona.n;aHHH nepBoro CTpeJIKa paBHa 0,7, a BToporo - 0,8.

HailTH BepOHTHOCTb Toro, qTO MHIIIeHb 6y.n;eT noproKeHa. A eCJIH CTpeJIKH c.n;eJIalOT no .n;Ba BbICTpeJIa?

o IIycTb C06bITHe Ai = {nona.n;aHHe B MHIIIeHb nepBbIM CTpeJIKOM npH i-M BbICTpeJIe}, C06bITHe Bi = {nona.n;aHHe B MHIIIeHb BTOPbIM CTpeJIKOM npH i-M BbICTpeJIe}, i = 1, 2; C06bITHe C = {MHIIIeHb noproKeHa}.

CHaqaJIa peIIIHM 3a.n;aqy .n;JIH CJIyqM, Kor.n;a CTpeJIKH .n;eJIalOT no O.n;HOMY

BbICTpeJIY·

JIepeoe peweHue.

IIo YCJIOBHIO P(A l ) = P(A2 ) = 0,7, P(Bl ) = P(B2 ) = 0,8.

C06bITHe C = Al + Bl COCTOHT B TOM, qTO npH O.n;HOM 3aJIne MHIIIeHb 6y,n:eT noproKeHa XOTH 6bI O.n;HHM CTpeJIKOM.

TaK KaK C06bITHH Al H Bl COBMeCTHbI, TO

P(C) = P(Al ) + P(Bl ) - P(Ad . P(Bd = 0,7 + 0,8 - 0,7·0,8 = 0,94.

Bmopoe peweHue.

IIoproKeHHe lleJIH (C) 03HaqaeT, qTO: B Hee nonaJI nepBblil CTpeJIOK, a BTOpoil npOMa3aJI (AI ·Bl ); HJIH nonaJI BTOpoil CTpeJIOK, a nepBblil npOMa3aJI

(AI· B l ); HJIH nOnaJIH 06a CTpeJIKa Tor.n;a

C = Al + Bl = AlBl + AlBl + AlBl ·

nO npaBHJIy CJIO:lKeHHH BepoHTHocTeil HeCOBMeCTHbIX C06bITHil nOJIyqaeM

Tpem'be peweHue.

Hail.n;eM BepoHTHoCTb C06bITHH C, npoTHBOnOJIO:lKHoro C06bITHlO C. Oqe-

BH.n;HO, qTO C = Al + Bl = Al . Bl = {06a CTpeJIKa npoMaxHYJIHCb}. TaK KaK C06bITHH Al H Bl He3aBHCHMbI, TO P(C) = P(A· Bd = P(Ad· P(B l ) =

== 0,3·0,2 = 0,06. CJIe.n;oBaTeJIbHO, P(C) = 1 - P(C) = 1 - 0,06 = 0,94.

307

ECJIH CTpeJIKH .n;eJIalOT no .n;Ba BbICTpeJIa B MHIIIeHb, TO C06bITHIO C 6JIaronpHHTcTByeT 15 HCXO.n;OB .n;aHHoro onbITa (cTpeJIb6a no MHIIIeHHM) H3 16

B03MO)KHbIX HCXO.n;OB. TaKHMH Hcxo.n;aMH HBJIHIOTCH, HanpHMep, CJIe.n;yIO:W;He: A 1 lhBd:12, A 1 A2B1 B 2, A 1 A2B 1 B 2, AIA2BIB2 H T. .n;. II09ToMY npo:w;e Haii-

TH BepoHTHoCTb npoTHBOnOJIO)KHOrO C06bITHH C = {Bce qeTblpe BbICTpena -

npoMax}. IIMeeM P(C) = P(A1 A2B1 B 2) = P(At} . P(A2)· P(B1 ) • P(B2) =

= 0,3·0,3·0,2·0,2 = 0,0036. CJIe.n;oBaTeJIbHO, P(C) = I-P(C) = 1-0,0036 =

6y.n;eT 3a6paKOBaHa?

a IIapTHH 6paKyeTcH, eCJIH cpe.n;H 7 H3.n;eJIHii 6paKoBaHHblx 6y.n;eT He MeHee

Tpex; He 6paKyeTcH - eCJIH cpe.n;H 7 H3.n;eJIHii 6paKoBaHHblx HOJIb, O.n;HO HJIH

.n;Ba.

IIycTb C06bITHe Ao = {cpe.n;H 7 H3.n;eJIHii HeT 6paKOBaHHblx}, C06bITHe

npHHHMaeTcH} MO)KHO npe.n;CTaBHTb B BH.n;e A = Ao + Al + A2. II TaK KaK C06bITHH Ao, AI, A2 HeCOBMeCTHbI, TO

Haii.n;eM BepOHTHOCTb P(Ao), HCnOJIb3YH KJIaCCHqeCKOe onpe.n;eJIeHHe BepoHTHOCTH. OT06paTb 7 .n;eTaJIeii H3 100 MO)KHO n = Cioo cnoc06aMH. C06bI-

6.4.22.B o.n;Hoii KOMHaTe HaxO,1J;jlTCH 4 .n;eByIIIKH H 7 IOHoIIIeii, B .n;pyroii

10 .n;eBYilleK H 5 IOHOIIIeii. Hay.n;aqy BbI6HpalOT no O.n;HOMY qeJIOBeKy H3 K~.n;oii KOMHaTbI. HaiiTH BepoHTHoCTb TOro, qTO 06a OHH

OK~yTcHIOHoIIIaMH HJIH 06a - .n;eBYIIIKaMH.

308

6.4.23. MOHeTa 6pocaeTcjI,.a:o nepBoro nOjlBJIeHliji rep6a. KaxoBa BepOjlTHOCTb TOrO, 'iTOnOHa,Il;o6HTCjI 'ieTHOe'iHCJIO6pOCKOB?

6.4.24. IIPH BKJIIO'ieHHU3roKHraHHjI ,.a:BHraTeJIb Ha'iHeTpa60TaTb C BepojlTHOCTblO 0,9. KaxoBa BepOjiTHOCTb TOrO, 'iTO,.a:JIjI 3alIYCKa ,.a:BHraTeJIjI lIpH,.a:eTCjI BKJIIO'iaTb3roKHraHHe He 60JIee Tpex pa3?

6.4.25. OJIeKTpH'ieCKajllI,enb COCTaBJIeHa lIO cxeMe, npHBe,.a:eHHoii Ha PHcyHKe 68. OJIeMeHTbI C HOMepaMH 1, 2, 3 MoryT BbIiiTH H3 CTPOji He3aBHCHMO ,.a:pyr OT ,.a:pyra C BepOjiTHOCTjlMH, paBHbIMH COOTBeTCTBeHHO 0,10; 0,15; 0,20. KaKoBa BepOjiTHOCTb pa3pbIBa lI,elIH?

309