# Chapter 3 addition - p1-1#51 “'0 will use szmshmeu...

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Unformatted text preview: p1-'-1 #51 “'0 will use szmshmeu. Sziuplmnuum. Bzhuy. szII. 6 PG. ['1 SB. 4FB. I St]. Ifthe probability of i1 random choice to he e1 buy '15 m hr: mﬂepemlcnt of being a1 freshman this 121 equivalent to HEB] =[P'[F)P[B]I 4 _ 1 1H IG+1'_1E1+1'1E1+2' Solving this gives 1' = 2. Problem 3.53 (page 112]. I31.) MEL-51' Lwc- dm'ﬁ yen. Hm t-iﬂL-r-r b-r m. thr- c-rig'ml print-r. 'thl" prin- p-l'm 2 1mm or 111.:- priw nﬂmm 2 1111115. It ﬁL’iﬁ-ﬁ 1hr- m if and oak if it gc-r-H up on m:- 13:13 and uni-mm c-n. 1.1m mixer. 11m :31:- mt- Ilﬂar- ﬂﬁﬁ: up 1511.. 11mm 21113. and. ﬂu:- unﬁt-me. 'Ilw prabab-J'Jiw ccE' 1.11.15 lmpp-mjng 1'5 2 X 111 — 15]. mm:- thr- 1314's m mdrp-r-ndrr-nt. (1).] If we watch for 1.1m days. 11w pcmibk It'an :i:1 valur m -3. -1. +1. +3. In. mud-91' 1c: rhimg-r +1. cunt- has 1:: haw-r m' m:- 11p days and our 1.1mm 13:13 can of ﬂu:- 1.1m. 'I'lmrr m 11m ﬁﬂ'ﬁ ﬂﬁﬁ mud lump-m [Dirk the day wlm iT. gc-rﬁ damn]. m-rh. wiﬂ. prehibﬂity ‘IFICJ — pl]. 54:: ﬁlm-59111.9: 11w pm-D'Lﬂﬁliw of 1mm grain-hi one 1:11:11. am": 11m dawn ccE trading is ﬁpﬂﬁl —p]. [n] On:- ﬁm rambw ﬂJiH de-milg': :mu law 1.1m digs. and by [12.]. m:- muﬁL br- ‘TJ-luﬁ 1:12.55". Thus the ﬁrst day. man:- all days :31:- eq'LmJL? lilac-1y 1:: 1:9 mm. M'Jl lmw prahbﬂity 233 L:- lmw b-H-n a pﬁﬁw dag. mm I'm c-i' ﬂur- Tim-c days will 1mm 1.:- b9 pﬁﬁw. .ﬁmﬂm way to nc-lw [c.jl. wlﬁrh 115m mndiﬁc-ml Nab-ability Inc-m t-zqahriﬂgr. in an follnwa. DH; .5 br- 11»:- ﬁrm “'11:: ﬁnal day is p-cmiw". and F ﬂur- ﬁ'FIIL that w m’ﬂqr- c-nr- Imit by Tim {-1111 CE 111-:- 1111141 1.1mm We m mm 1.: mmmm- FILE | F]. 135' Emma's tlmm. FEE] P E + = P .F -— I: I n I: | E3: PM 13111. we Mr PICE] = p. and w:- kmw PIT] = 31:?[1 — p]. familial-1:.- to part [a.]. Finally. FEE | F] = The pr-D'Lnbﬂiq' that m' one of 11»? 1.151. m:- dmﬁ 1'5 mum = 2p[.1. — p]. Uri-1.3"?!) Cam-mg can. 11.:- miﬂwﬁr on the HHS of Bart-5'5 :t'c-nmﬂa r1.me 511-5: 1:: 2 PKEIH=EP[l—Dl'm=g- f3. Lava-h; nghgp 9W6 d a rid-«oh. m L434 E XL: Mk tf'buw‘r r?“me D h biﬁhm U . (gm; --’P(137— Pl) W3): 91, Aﬂmras "BI'DJm 4h: ﬁMJak L=>Pan13).—.ﬁjv_,_d (a) H wk m [we em mm M ‘Lt 1km “‘ 5 Prune): Pm; + m)— P( rang) 19:) (“Manama ‘ saccﬁag'm. C5) ?(BW"9¢V& H44 cu {task m that) Problem 3.62 (page: 111}. Wiﬁedidmaatafﬂmln-gicafﬂﬁapmblernmdamaeInm' abbm'iate ﬂing here and there. I will also 11-111. 1:11: the gaplﬁm pure-yam ta- draw pictures beam-d what 15 alrmiy 111 :mu: Lamb-Dole 111 11-11-111 web-1mm. we have ﬁve switches win-11h. we amme are mﬂwlﬂy magma Le1. A.- b-e The event "Lhe 15-1l1 snitﬂ 15 rile-eel", 111.111 Pﬁxlij=pi. Finallggl-ELEb-erheevent “emateanpamtlmughﬂmdreuitﬁmnﬁm B". [a.] Hene it is chain-115 that swimﬂ #5 1111.151. be daeel, and. ﬂea ﬂat, 11111e 1111.151 have either andte‘tma #1 and. #2 are cleared, DE. snitﬂea \$5 and #4 are b11111. deaai. If we 1111-1111211 1.1115 1111-:- 511-1'11111la1:E we ﬁrst calculate by c111 Lhe ﬁth. snitch being dose-d: P131 = FEE | 11.51 \$111.51 + PIE I :11) air-111- We 1121.1111- F[E | Ang = I], and PICA-5.] = 1:15.. FinallyE 1111: 1.11531: abcwle uanalalea 111m PIC-513a] PEEﬂLn-r'bIIl-J EA: nil-4.] | As.) PICHL F132] U H: W143]! be reﬁt-Id ﬁlial-widened! = nfhj+P[ﬂgnM—P[thﬂznjlzndiﬂ = m-p:+m-m—m-p2-m-m- It ieittpnwterrtteneueethat we arenetm'ing lteteﬂtatE=[A1ﬂA1-]U[:lan:hj 1'11 the Eisteftitielast suingefequatimte; .t'atJt-elrE we ere-enh'm'ingﬁ'r‘lxh ={ICA1FIAszU [A3 r1 A43]- r"I As, because we are deeJiztg w'jﬂt mmiiu'mtal probabilities. .altegeﬂteaweget PIEII= EDI-32+m 454—151 are-m 454] '15:- [1).] The'baaleidmeai'ethe EﬁnlEhH'EﬂEileﬁILlIﬂJ efthie pmblambut ﬂtelegeed? the circuit is a bit mere map-heated. Fell-aw the lent and solve by mditie-niitg en. the event Ag, mat is, an whethat' er nun-t ﬂte ﬂtii'd switﬂt is closed. Then PIC-5'] =PE-5' | Ha] 'PIC-r'laHPIC-E | AEII 'PIC-r'iéil- Note thatE [F ewttﬂt three is NOT deeeui [event .45]! the-1:1 the EUJTEnt has te ge- am the tap {event A1 [1:14,] 43-: the b-ette-m [event A: [1:15]. This \$35 that: PEI-r15] = Pﬂiﬂtﬂr'ltlUlCﬁ-zﬂﬂallﬂﬁjll Pﬂﬂmﬂ-tIIUICAzﬂﬂ-ailh 13a“ mﬂmﬁ eliminated-'5 = In 'P4.+P:'Fe—P1.'P2'P4'Fe=ﬂ5 in pen (a) abate. On. the e-t‘tter hand! in. the case when ﬂte thiiui ewt'tdt is ﬂawed, we get current titre-ugh titeqtreterniiﬂﬂ'ﬂ-Eoneefﬂteﬁietereeeendswdtdteeiedeeeuiietmtﬂluﬂzj.m me of the ﬁemt‘tt and ﬁfth switehes is dose-Ii {event A4. U445]. This were that: Piﬁlﬂzil = PiliﬁtlJﬂaIIﬂlCﬂ-tUIhJI-r'h] PEEAIUﬂailmCﬁ-turhllil PEALUAeII'P'IC-rhU-ﬂailgbemﬂw mealtime-a = m+F2—PL'FZJX[54+PE—P4'm .altegeﬂter, then! we ﬁztaJJgt' haw: Fiﬁ] = PEEIJEJ-Pliﬂail+-P(E|Aé)-PHEJ {[1514—32—31 -pzil><[m+m—m-ps.J}-m +{m-m+m-m—m-m-m-m}-ﬂ-pﬂ m-m+p2-pa +m-m-pa+m-m-m {Dz-m114-m+m-m-m-m+m-pz-m-pa+m-pz-m-pa+mwish-m} +ih-pz-m-m-pa- Him donlt have m camr 1.11:1: out to the bit‘Lﬂ' emi: I donit ﬁnd ﬂds last mimiun panic- ularh' mhgmemmge EDI ample. W62— '2’— (ca) _._/;H_.x; __ __ _ /_.._ g“ L MIME} 5 L1 .‘5 Le»: 25mm WM 90% t‘ 6 CW. m P(OhW W): Pagina) 9 (EBA gﬁjﬂg) = [rﬂgmez- 1‘ PC 0 - mgnisa “MWEA‘W; E: m We 5:)er = (NH M, *inamgr +’PC§P}?(0.AW’rWI 53:") : 136957 H Qua-1,) p [avg-3)) 1 F‘(E:)’P( Emaw (was); z 1’3 (Pt *PL-Pm») (mwrwm + (H‘s-)C Fiﬁ-{4" W! " [’1 mm Fr) / Pg 111 #53. (a) P|P_JI:1 1133:”:1 PI] + P| [1 PJIIPyII PHI + P| [1 Pg :“:1 P:;:IP| +PJPa|I1 PIU PIN + (1 PIFP2|I1 Rail—P4 + [1 PIJ'Il P2395134 +P|P2R3E1 Pﬂl + P|P2|:1 P:5:|P1 + P| [1 PQIIPEP-j +|I1 PI IIPQPEP1 + PIPJESPI (11;. RH + Plﬁgﬂ. + P2P: + P2333 PIE—’34P: PIPEPIP': PIPE-REPﬂ PIPgﬁaPﬁ P2P3PIP: EPIP233P4E +3P|P2P:;P|P1. (ﬁll EE’II'JJEIII PI'H .i i.- nix _. PWW Q‘s L! ""”' ""‘"‘“ *j’ 1}-.~.»,._.__/...._; r 5 ‘1 fPC 5W3”? L: Li 0W arm n1: .__ 1% El AE‘JIElnEQ U [93, nﬁQJnEs') : a: . Eﬁ-W‘Q/ KNEW) + ’r’ (mm, d~ PL :3 man ant—@355 : Elf.” “Chan's... -— am.m Whit” pjﬁ»P.PL§J3 FM 1:5 WWW. {9'} Pb“! :j m 9&3: [’ng35; w EbAgL-y 3 3'(%-)r= ‘lb fry-IF U) H b51935) = (1-5)“ V3? (L) Knacg 3 by: '- (gyﬁ—lfrr' 7. M) “a u. H (v) (Prad- aggl- fgmc) = “WELMJL. I, 655’: W 713 MT- :Sle. Pub {,1 Sleifumg 4551M. \$N£aaﬁ~5awg2 pm warp (MWth) Tﬁ‘wnﬁc W“ 245?“! A w 13 x: 2mm; MM, (9») W Emu?) .{Z‘ergam care. {Stayed} = F(I:A=:B M: w 143% Wm“ W‘Bﬁﬁﬂ) ’3 LP‘ﬁ-r) Wh-ws» _ — 1P£"P)( 9" 4- (1-153?) '" 21’{"P)( 291-212 *5) Cb) "Puma: f HAM; m 2 ham?) “‘1 mg - 1: Z Wu“ “H . __ um Mr) [Qt-r ‘ 3' w“ T /‘ IntﬁAM} A'Ull'f M“ w ijw I k—4 1. —; a; (pm-ff 2. P L) w J “(A 0‘“ a : F p Z @PCI—Pﬂ 5” 1:- Pi- gumman «h»; Wis-4:.— W433 :- 1PM?) ’.' ﬁfb ,R f... m??? ‘h. ﬂ is varWt/f “1’1 < \ w . We. E L; Ti!le f. R 1.11, %2\ w (cs) Poe.) == PM) Pum>"'+FLEa-P(:zmy -= 5% £— + sug- ~41- 4.5::— (a) HAIR—TL) a; HAL-H: 119») (P (mg L gaiﬁ‘vp-LQ "‘ f{l— 52qu S‘Pam.. Au. 2w Qubﬂcﬂ'r j ibghgag, ﬁﬁm' ENC-w Era-Em I‘Sn‘aluﬁqa 35243. {a} A C 2?”;le h MEWS) Pﬁﬁgﬁl'ﬁhuh '. a ‘5' (Mg—ms (w gWu—m W W me= EW)*3PCU:3) WWW) 45mg) 2 3 + ’Wma; + Wm?” 7 3 "‘ BPI'T”) , WWMR 5; ijﬁn'n Mama. Mm 121.51% “IL; was “inning; [4:12, 4mg M 604.56? maﬁ-CMJ" Pg 11!} #17. [n] They will all he white if the lurst hull witlnh‘nwn from the 11111 [when all halls are withdrawn] is white. As it is equally; likely te llL‘: an}: ef the 1.1+ m hull . the result ﬁJllewa. [h] PKRBG] = {ff-“(r + .7; + y) PIIRBG Glﬂﬁ-t) = {ff-“III + .7; + y) < [:Jf'lIIF + 13)]. Hence. the answer irs Fir; F? .r; — + — (r+£:]||:r+h+_r,r] r+h+5rr+5r ...
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