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P(AflB): P(A).P(B):0.5 * l/6 = l/12..atUJl4*,J1.3-: J:!t U)l Q Uy .P $**t,1t^r-t,**i ."er, qs i-I" l'ib .Y JU"

P(FF) = P(A{18) = P(A) P(B):0.5 * 0.5 :4.25y I*tJt t$j Aj.li",an Lar.- d GJ) J^; u-f ,=--*: .eLi* l'j elp Y c,!r5' o * $jl:,e .f JU,

*#.fri5ffi":,Tt'if,ia: i'P(RR) = P(Rr 1^1 Rz): P(Rr) P(Rz) :2/5 * 2/5 = 8/25P(RRR) = P(Rr fl Rz O p*; = P(Rr) P(Rt P(Rt =2/5 * 215I2/5 = 81t25P(RR): P(Rr 1^1 Rz): P(Rl) P(R2IR):2/5 * l/4=2/24P(RRR) = P(Rr fl Rz O Rr) : P(Rr) P(R2/R1) P(Rr/Er0Rz)) = 2/5 * 1/4 {q 0 - 0

'"Bo ji "An .!Jr &F"l .Jt**t

o P(AUB) : P(A) + P(B) - P6nB)

€JdJiJl J3c.r.fl*i g*l;i..l.p.i lqJtolrIf dtlJ*aLr4

.tktu* "8" -rf nAu !4J "Bn jf nAu bb UfuJrc>r

A, B 4Plr{l e,t-i-!tc,*1

P(AUB) = P(A) -r P(B) (P(AflB) : 0)

P(AT.JBUC) = p(A) + piB) + p(C) @(AnBnC) - 0)

P(Az- Ar) : P(Az) * P(Ar) : P(Ar) s P(A2) :.1!e

l*{" pLr!JttP

ArCAz blu I

o

P(AflB) + P(AOB') = P(A) :uK!i olui B, A J*i' r

Aro Az o A:, A+ An :aoitxll ert-r-!t ,pa jl.r*i l*+ ,'o A ltf t:1

P(A): P(An Ar) + P(AfiA2) +P(AOA3) + ....... +P(AnAn)

Ar

DAr... A,Az

Th6ordme ou rdgle de BAYES .i{tt ir"rb yi UJtr.Jt*rrlt lrrl,i

Uita"-r**t;K;o t.,:t*t.:,i- k4t L+ l,rti, ert-uf 4n c. . . ,As . . (Av cA1cA,, ;,(:.1

*.,,1 $tgA,:rit^i" lij rAk crt"r-!t g ,r€l Jir-!, e* f dL-+ u .r*- A: ,f,) qo*-u!D

:o! tJAr e$t 6,rP O.e 4ien JLbl

Dl A t ,t\_ P(A)P(A/Ak) _P(A^A.)r\Akt tt1:;;-:-I_=,pt A)P(A/ A) P(A)

dr.,F G! $Jl Ji":-Vt a,-pi a;bft oj,o ,r*;U! .Jt -:^ (At) t. e.,'u o3(1 oi JL^b.l ".,L"^>

.(A) J*T d,r-

AA

A2

.;*r+fuE, *34r.s 2 rs

1;; #Jill .!3r,cra JSt.lgrrli.J.f.i lqlUirYl AIJ*eLr.

d6tl,r *:(! J*o .;Ft UYo \. el *ty e.e a*-t*^U ;lfq (Ar) ,*K, a:*,i.rLbj :Jt*

aYoo e ,\)"*l;+.r4tai!y'I &; .Yoo. (A:).sf!b _orllt,..,, %r, & qA2; trt.r*1;a,;l

.%t (A, atuJlg;rlj %, (t> a;ulla;;J fUrtq; L* ,-r.!ll

Fr ) i,ii r*.4 dJitiJl *.fr| y..p 0F oi .;3!t .r;l;-t .otL".{ tr ,Ji &." ,;W;K;^1 ;ryU .r"i,"i

.1%oy,{\t d krJ "t-L+.!tL; 0L c.,gs.!t.r},ultsJe.}r-, ,*Vt v %1. U

og(l i,f JLb-tC. drlt3 g3it.ijl o.,r ,ll o* (Ar) ;*-r4t ;ub:lt oF -:i Jt^.Fl .---i . \

.A3 JiA2 ..lhtt ,t-a'.e.,),$l .>!kr-!t p** **i .f

.ot!*l t< Ats ai r.:,)\-!.1 LF a tJlrr";rrs itu Jts irl Jt"j'-r.----i .r

p(A.111= !G)P(A|A') =, . ,0'2*0'05. , .=0.238Z'o=,p(A)p(A/ A)- @.2* 0.05)+ (0.: * o.oz)+ (o.s n o.ot)

P(,4" t A1= -!9)!(A/ A)- =

0.3 * 0.02

P(4/A)=

E'u=,p(A)p(A/ A) @.2 x o.os)+ (o.l * 0.02)+ (o.s * o.ot)

P(A)P(A/ 4) 0.5 * 0.01

(P(A)>0$r&)0)L&.-, ,:ltl,r.lt,ir51 t -rr

= 0.2857

= A.476

Z',"=,p@)p(A/ A) (o.z * o.os)+ (0.: * o.oz)+ (0.s * o.ot)

.iytiJl .r)F oJl e 43 i,J* iri.3* ;5!t Jt -s-!t .ri .y#t u ,&.a;r*lr e/r.utrr rr!1":-rJri uv P(Al/A) + P(A.2/A) + P(A3iA) = | e!1"l:'"Vr 1r* .y

.d/)UJt

I iL4L!r" ,2lL*:t4 Jl^:-l .fp(A) =frgoyqA/ A) = (0.2 * 0.00s)+ (o.r n o.oz)+ (o.s * o.ot) = 0.012

i,.p1*Jt

.-otiJf u, -fi"^bV & J#l&..rYt^,c-Yl Je e yN u,l-Kavt^Al a,r"bj lu*;,.u:1J*:*l lirLll oj4 '&j*Il

rr5rr) s P(2) n P(5) :y,,9*,J d "o 1 Y a*jJl" Jt^:-l :Ju^ (et) "J" 6.tV ,f !+ fl gttilttjtlP("2" n

P(*s*Uu2u): P(5) + :,, ql ,2 " j Y a*3Jl JL*l :Jur "ou" "ji "bV f V* U :l*Yt ;"_,

P(2)

P(O = I -P(A) t" A r^Kr" 6:V,f Y+ A ei Cr p*ct;o

..rYL*"-Vt "rg;.-U!l a*Jl .roFlCf d14.,. * i,i,ts{,}dl U,6 J}- "r- P(AOB) = P(A)* P(B/A)

=> PIBIA; = PlAr^tBy / qey

- P(AnB) = P(A)* P(B)

- P(AUB) = P(A) + P(B) - P(AnB)

€J*"iJl .13*r.c ;Sl,.l grl;i ..l.p.i

- P(AUB) : P(A) + P(B)

t4"dLirYl crlJr-ab.

f(AnB) = 0): csi,)l*k" 0iirtl ,re(- t .r-

:er.rlt ;s, ;o ,"13!l ,;l d altt" B3 "tlt'idrr" A ,r*; r.gy \-JJ; arJo3 *r; .eJt*.

"B-A, A-B r AUB . AnB,A, Br A

A = {PP}, B - {PP, FP}, A = {PF, FP, FF},AflB: {PP}, AUB = {PP, FP}, A-B =(D, U*4= {FP}

di,'.l4Jt

,;'Xl4eTt Cp *sr**Jt rr**tt

,,lfJt ,"auc *i Wt* Jt(ll Ju"rl.r kLl* ir*d-d e)l*>,)lJ 6y ilU 3- 4 7r.:^lt )+o

Jtî*.!l ;re.-i 1p .dA, lb3 (.d! JaJf) Jt^bll ;r.,* &-*tl lj.t p.r:',.:*; .Qa oUlLl! 1ert.i-!t;

& ,hb l"i ,J,pi y Lp ot-rl J)L* .r eU5: iFl Ji ;r-!Jt aJ,F;Jl f el dJl aritCl e,t.r-!t

.a,.Frll & Jlj*. ,Flt ;{st q*o,'Jl J,tr-!l J*L:j fr#*J

4*E t t-r. 1a*j

a"t' Vj g:*j, i,t+ C a"lt ..s!11 glt+ u# ,F.rYt^;-l (f J.s!.,ri;r*:ît (t 4 €lt.uv u.7,! ild*leJb;JlJ*i Li,F ra.itr, c,t.r-i

.rre rxf & &*Ll Jtî*l**'-i .dy q& aJ.5,r^y .Jtl

P(face fl face) - P(face) * P(face/face) - 0.5 * 0.5 = 0.25.

oJgaP(face/face) = 0.5

i4tsP(pile/face) = 0,5

P(FF): P(F) P(vF)!i9a

P(face) = 6.5

OJJ,A

PGP): P(tr') P(P/F)

Pen = PG) P(F/p)P(face/pile) : 0.5

a;xP(Pile) = 6.5

J,r.L3S

P(pile/pite) : 0.5 P(PP) = P(P) PfP/P)

dJcJill tJrr.a 5tJ U#lJi.t p.l l4Ctairyl d,rlJ.abr

.dt3^i"Jl &.!iJt pjg.ir

! er"r- Je &J^ri U.;l :j"r;It .-! cir3r$ ,:\ e;"a ! er.rlt Jlg ! y'la-c e,.r* a"tlOl aL-Xtt .-*atrLa' ;z* ***lf t"et -l tI .:.tf a6r g\ -.!t ,Q r'6J dJl 4rjfl .C* ! fliq.- Jtf l3i t t4* d-J

t r;*t .'eiJt tlr &; r:i Vl &rtc, ;J(l'6* !o'.airl,-\L * aaUf Q "i y ,:i ;ryIg .rt*".o

',,i W ittlll o.r,o Ji c,:1 .,t*i :Ju ;KJ .*ltt;l *-l fr r,ai | ;i,j,l li$ r4i.r.,, .r)1+ d"lJl Jtl

.1o; a*jJl ;r.-\it' J,e J4.d* Lt' lil d,J Y Lip.:!y 1 rj ,--(. Ur9 ljidJJi.' ... t.q l-li,rt ,i"<L

orr r,..) dr$l d,^ lr* -6 tp r*"1' *t l5i ts ,i,-p LJ s* (P(o) -116 >ti; P(X) r"* eUit

.r!t^.-!l & Wy.1000/6:.rJl6" 1.r* l*j.-rjKr.. 1oy o*|l & $-elt *tr.r.lo.ri iJ* (yt.".b.!1 a.-rs" ,'*l qlo .elbi eJJlr rol$Jtd.,lr-!l eV ,),:.*lt9n

a.ilaltriiSLlt c,Xb'Jl )Je qrL..'

.surjection flsi, Jla"j)ttl Ji;r(Jt ,!t tt .:-tr,.-,tJ ulrietie ,r,!9 (:,t*;;:b ou*/t Jl i}l?)t{

surj (n, k) = k [surj (n-1, k) + surj (n-1, k-1)] , (n, k > 0),Surj (n, 1) = I , Surj (1, 1) : 1, surj (1, k >t; = g

:.r-!9 ,rl*ia.jr!t ,rl" +SU ,)E :* ai Jt^:-t -*i 1t; Jull 4 :)tl"

: 3,r l-)ill .r!t.}'l r-t-e

Surj (6,4) = 4[surj (5, 4) + surj (5, 3)]

tf'**JlCf ;l*L -'t"'":' Jigt'* J-Ui etJSurj (5, 3):3[surj (4,4)+ surj (4,2)], mais: Surj (4,2) = 2[surj (3,2) + surj (3, 1)] ,

mais: Surj (3,2)- 2[t*j (2,2)+ surj (2, 1)],mais : Surj (2, 2):2[surj (1,2) + surj (1, l)] :2(0+l) :2:> Surj (3,2):2Q,-

. 156014096li! 9 Jt^,:-Yt

+l):6"...nk

2 J 4 5 6

2 2 0 0 0 0aJ 6 6 0 0 U

4 t4 36 24 0 0

5 30 150 240 120 0

6 62 540 1560 1800 720

- l. -

Ch oyk* Onu'

*W mn&h*^q-&ic"j +he-r43 ef p"-t^}'i\i5 wcn-s

**+^,"pA \rJ $*** *F* .!. rofr..,bhurn**r'et4nrS \\.,ris*-

.*poJ (*zs* t662) **j f iurre- Te,n** (t6*t'f66t

\,JI*4 b Succ**d**\ '\

A*r.iub q-Xq.F'T""t"bilS$

F-- Cbr*^U 1**\rltry ?rrJ.\*s{S t"ruo:\rtg &te*'

'FA*Iri\rv5 A*5 t*?"* M %ede*"\**ofu

C*ay "5 *-rb '=se-o.r-cL*qs 'a's H%t*"\B*'e's\i

o*J \)*Mettr- M *ga*\\*\ry e't ff\*rL.o'*k'J *a'1g

^f ryr-b*hr; f5' T-&S, *?'-\* t$-kis \ s

e s-\-*-L\r^)-J Lr*,r *h "f **p\**of,bs .f"h* {i^t}t

,*fPlrbo-&hns i\ *VH o'ts<q ?** vnwsi* A*o

"b*tos'wu^rh* yr*J*&'urr ,;C "fr"J'Y lL r'sps { n** *,,*1"co{

.{-re,ctnt*'*s

J^ ,+.,|,\* Nlu{*, {are-- q,lr*l{ *uub ffiffiHJnF"*

e-\cf-er.\vr.^"\s S."** -pyk*LI^F€ \*pd. { Vi"ul ^

tnffi[-rrtrffi

+\"4k' +f-*-

[:tk"..

ru"?i,tifrevrs

r6'hX'ferVn -* :

*+h;s -ferr4 f*s-J i n F*tA; \ i# +\"tet5 bo

d

A**ci,\*- f\r+rs'e\ *'S \r-:t* whstr--

o..^S C-qrnc. \,> r{o\- ko**n r\t ^&tte'rrt(* *}l$n

Cor*.rinl-yL, tF ^nf,'*co

frecerss.v\-& \*.&" {* "*}t-d*pu-}r..*-,tkc*\*& or&(evtes ' r^ .L\*--q -

t Ct.t\*A O\\k\o'w\ir5'' (g"tl r-lL s*,-nqL s\ctc-r t *Tq* C*\\ * *\\H*1$ *\ $<*

ss\L

"s'ffiilrytr[K#'*['sryL'' -_Jf, s.*\$,*b -,{ +-Uf'* =='o*'\L "T*

- ! tlNarrvrafl t ur-!e'*1"*l'( J*-"t'- e'r^-&cew*-s bJ t****

Cno** t*H""rt

**A *'q*n$rs bJ cery i+*f l"*.*t

ryu&(*vns-,. iu fur***{,t 4 ,WL*nul {'*t'--f';4y *sgertwrc'os-

r*1 I E r*\l'J o*flCo ' '$e- \"* X "\.*dh +\*-r"*yb, fi Ji* r

oo**g *f *t ,X exp.rirm-'t*' T[-'n +L- s"*'g\* qo* *# +h't

.e*lcyert'v*,.rh is -Pk 6- *'l*$1q-* S*t

fi.t{ --otria :}-7'' l', Lt3,L! 5/ 61 "-T*s'fu"(o''rns =funffi'

-th- *r*",;t f =- | ", t, , d 3 corra:f*J* +* +l''{ s4'\*erY\es'A-

!^q*o$& -{ C"- f*\\ l's ctuv\ €-NetS n*H,rLur . \} *o*S'h

c{ F,b^Ltfb .=-'F # a* "*"L"'b,*cq:wr's.*5 . r*'* ?Cll = f F''

'<i< d '

yCz)+p(t)t PC6) =

l

C*s* ./ e.ueqlx qr tu J**"; bJ

cpw e{*-n& +Ir*'y1|+L v }-e- { * s+^^J^rd

.()iln {.rrtls *T

Gns+y,^c&b"ots

L* *-.,..,* *"Jrs"-ffiu-^ +l-- ug -/ t+J)

AUtB=f *f x €A or x&bt

"-f A.--J B rs +L sdh,-

nnP z{*l x efr *Jz €83

T( E)" +"|-+ 3 +

:T[* &$"**e"- f ft *d B u:+k e*

frut\

A-ts ={ =lt €fr *A *{e}T* q*+ fr h *:&gt"l {b ., k}ri\\*., A c ts,n n

'=--_

4 A i: o\s- qn *t.**r -l f* TI.J1,

.lfris 4.Ls"* nr s t-t-^ ;JtIl fl =fi = f*l tG-Da ""J*+fr]

fi-n

4 .**"r eLw*"^f,<

+l'*c",rpl"*#,->[-=._{.--_

l: ;1 ,,./\inl't---./

,? s** Th*a1 ,{O

(r* ft *"A Ib

1"1 ir r \-o s.f :

-l):t,n- i vr.l*-rg*.4i-,r*-

\(L, \

+-l,f v).--

--./

A*,br"rs *J h..n ic *]f,-*'trqwrs -? T''t"L;\tlr

Ar,L* [ r*

Axob* 9- :-

F, ^U *,p,",wh' fr , ?CA) /o .

i? crvl q11*',$ ig Ce,r{qM }e o Ccrr"r, $^t^$'-=

rE.e&I+g 4+\.*x *\$*^k ts { (t'*-'\02,)={')'

Ax,b,,. s | -'Lr--:* .p,- a^vg iufi^ffisefuen* f Jti"n'**^t*o*A"A""

T(,Qn,) LrtAi)"\ "-\

ff"*"rnt L

?( $n;).la\

3S 6 <-R , #1*^ T('$ < Y(e) '

i* IF q4\ *v*^*

i't*s T*L'L;\0'1<)

fs inrp*rsi\\u- (*f5#) ,l*^nnwudr be- '2**,, t, . T(d)= o) '

ds,&,lu*

/k"ti-,,fr, fr,, fr,,* 4n't\

t- ?tni)I-.\=t

#-T{.- 3I hen't*n\ : *

-1{* \I h.o-orc}/n ,.

d-F-a' -' '

--'fr- .flka.+f'evr,r l*

T;" %""u*t fr,

F %*o",*F,

.ffi,' qg 'h^r#iv-$s A "$ri*, 96nus)=Pft)*?(B)*Phn$,art314^'t-t1fl on *[5;va--

{ \ \ f t il l*rhnYiri;,fi- d#t*& b**ut*nh C-\*ssicJ # .*"'girlc*l -V*bAi\,5,

is A"s cl*ss,,cJ Yr,l"-L;),t* q$sN.*rr'"s r,\"** c*,*,bl**. e*s-q*r**(J & i- ur K \

c{,{q ./S 1,9 (**& ff4'-ed*e*o'*s wL^,* di*-is '*'-\A)

w! * v E&,,*[r*u -t,-h "*J

;* e14 q c+*s( q-x'f.-ri'-s#-s-:t*

#*e*,r*wr\ vuts- "q}*- ti k*\'\;5 { -.ch cuun**

G,y* fVy otiiswk*,"* , )J'.*3*b*[nry 4,*n-1;*'fr Wf,n lJir*"c\^ii,

"tF)= u.hb*,

=*

l'u\- o;-*J, a*h*J ff ru

b\.,,4, r1o"A #f"&bl**J, -"d r hu.d$f*&nbl*..\ x"*q

q-T*y o{-:nr,t *p, -^d $-,# $\"" 9*tt**l5?*4,"b;1*s

C A ?erso' fr*o W* CI b['.J

A p ?ur tuv\ h,.v fff. fl *, fif" {3 f,{"*{'

6)P yer$*r h.* ne.iilw{ hf * n naY Yf- s bl**'$

@ W ?*^&ruotdt--h"6-trdf".-SB'L1'"& q

fl"B

tu&

q9

5a

.2 I.l'-lA+.4 bo

g*\,r-F'iu.tt ', * o 'p€c) s +,*w

Ce)

T(A n" .B)' ?@)t p(s)' *-r{- = *^7-ts-o

C$ p(n.ilA* S n*f,91, f("ifuBor66)= 98.,* 3* .r go 'st

G i'(o#F[9" l-?fur$* t* h** ",#

ff gI r\qeVe-Yn :'- f,a,. e't,ar-0

n,.'f(gfii)=

1f h-.*efe#r

@ YcAr*)= T$)'?t€)

$ T(A*s)= ?Lr") ?uq q

@ "(d€)

= "tA) XTr I

ffi**c*, f*, c\EssicJ -p.t^tj!aj

th**, e-vc^{*s h.rh*,, *-S As,

?(A)* P (A*) + ?(Ar) + (R, nni t P(Arnuil]-r ?(s,ftfr3\

+ ?(A,f\A'0H*).

h **u*^*= F,r"--fin,v]

(:*- r-

1Nn,)- ) ?rfi;n$1) *L?$inA;nsp)i:r -i6 ffin

,q"i'I

'- T "(

frifisifi*-{\${)+.--*Gt) ?(n,n*'nA*)/--l <1<w<t

: - ;$-t** qve--,*s fi -^A fb o\htrw- il^dT*,rir,&, eL^

+\* *-u*nSs fi***,t t{ c<r.q n"th"1"^'h*^}

ry t # &-

*.Tta*?rn\,"\rnl,\.1 V;re rt b*vr\LJ / J lo4*1 numbor/*uf(**"si..,.r^e* \'e/rrarur 'LJ 7 J '*- Gl"i numLord;f_Wf

-*rffiwt^htb is J*urJ L; ?fd. ffi*Kt 7*t*b'\Lb F cJtJ clcr$ir*,f p*5 *b,*# ,#-hsa-s +l* s*yLufg):

(-lqr QIA,.rl

Tx^,.r!* C*^s#-"$.dfr PG) - )-\A** _f Ttg$l6 {4 -"J ts ^{s

.f* {orf,l*-to

-E'F: ?[e)={ , T(R)=+

(t [J* Au (BAq) , -j&*.$*o,

..r T( Bfr)= ?tp)- F(A) 3

,|w* ea*ch* h **}" R*nd\."

*-J ?G") = b r h*-1,***.ut\r-- *\**?,- **-u\n '$ *U f*n**5 co*[i]*ry1gr

J,T',u* ('xJ-P*J.-*)

("p ncb ,

@ ?(fr8)* E '

n2_ls2.

)

t2*

?(r*) =

r *l-23

y(o)= b t ?cf)=L

?C$ + t{-{1tr)

IIe2

ffi ffiUb= paiu(reuq*bJ

f (A u B) = r{rqfi + "(As)

t?(n)= ?(n flr PffiB) ?*_pcn) = PdS)t Pwf$ J

P(fi.q

P(fL A") =

fo',.Ju ut*, *-F *k*t.k t{s:

-pd,- ip p *,J {b crrq o.v$ &ruo *-u"q&* s*o}n A}"ft

f s cd\*A "l^* Cbn&rhbn*Q

"'*t..tbRo*h,,,. ,"f rt?b* Rb.

8r g*&+Laf T(A) 7a t 4{..*t

TIF W.4ffit

pt&)'

qg *-.t\*"\ ;fu* c*"^&tfWo*R

-t,ft\,,b1$Ywc.l,k* f {d fl;wfJ"

T{ $nB) =')- 'q 3-* = 9=I?{* ffi*A

L u.**(*"*3***L t€ |

*r-;f.n6 oA - -[-=A =T-'

H*c-,Pcslu)= 4ffit=

C*ndtL,'.o,J "A^t'!

Q

S"rT*&* J*tI

Err*-Fs

$)**

@"te/d 3m= PLA)

{s Tfln)' *?W = rtm

*-]f.orem .,-- <="N\PtrU- St*

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Transcript of ryN.$yU$utrrir-;irtJl · 2018. 11. 3. · fJiJll Jjrs.c ..;E|J gd;l .{p,i!4Cllr3rYl &lJFbLr.r:1 :