ࡱ> zayuIӘq( r?'N`!H9Mz1vdr@2MSxڥU?hQ%i/IӴ.)M7 Ţiq*LRiAb* T(:-N*{!p~}?Aл8@ p };gLau]yf3%κ1R9!FiȀ$Dehu{p{g]Xdop\V}y8__6$6B<&y?G0*>cO7: ƫS```Ւk~s▃#>9_Rҭsz:0Vcەfp o,"s#.k=I8yË$šUr;yҁ+"_"AQ<+:'Yuzv/Ϩ;)SIѦe#4O"C1JMS/)7}-oh5i<(cF^%L|Tywح ofƽyv/㰋c<ziZ;L&izB-ߓ7%+94nLRhHa27MfDO"JFIFKKMSO Palette C   ")$+*($''-2@7-0=0''8L9=CEHIH+6OUNFT@GHEC !!E.'.EEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE"!!1AQqa!1 ?F3]'IƓe5,J$3?O 5LXyYL4tO%fxM\DXL`: a2HS=rtd+f\UtV5m7L?cf7 `Zx5\k`!iIf/x` hn PxڅRJAyI V*^P=EX3B'RY#X5[+xn207?!Fu0g hŃxpKG)8)J0rSk:3$mܞjGrv gO }EK@յg3;y*he]Z]s zkK7(KF&dîΪWzX࿉JNz{)/my`!{H9/ecs{j!Ixcdd`` @b1##X`=F !#T57LB@?& sC0&dT20$UfJk2a\& Ma`ٯ F\1jH'4hm/D?#\ n?K)~Q~eM-VK-WMc`%g 8B >);%| ~΃ߊ U^ U-z48@m|Y84r28xv0#&\H 3X|X`!榸ժҴ੆4@`dSxڥSAKA~fM[-WS/-E :t0FRB/]:x7n:]ڱsQ6ofZ7#\}o}3f $x"CȘ0t:23effG|`5PR!X7EtO(԰D Sj'͈%* Tک ψ_0'#cro>$4L[2<o#7gQu48RWXGähLDr/ {fk8xx/pe Q/WrepOdw+YrpV6;m)=h662yAYPzf+ݣ]-i\\د=$RL8z{ڮlo)o<(XvRtL*U;K.y"z`!\Óu`HbmxڍR1KPw/iMZmP ⣃(.Nl)j ) ƊH6Ws]ΊƻZw p䭠MA,(H{6ĂTPyyY3XIH[(Sh;i>Ol}msjxHWV l[| ]{a*>0W JWx[sd3|DZQFMIQ`dcL7 y?{Kkq]Ua'hlnLIi{ nȟOR̩&N+ye+Qb1.'teJրq \3O9=dJszx7~d`!@ B%X5da/Z@ `PVS]x]RMK@}3IҢ!*҃4={h{Rl{B@B k ??/=+gwXa&3//3K( >.Bl&8uvu).יZbUWQs$3@ TU_T6ϸіƯ}~l۹ a2x,_bTyy8o rm)YWSڭG̯G)_^DsZՋhj\n{7.,Rjzbʹ),"6dl޴TM'M7338gG:j\x8 B`]$L"(  l ] Equation Equation.30,Microsoft Equation 3.02Equation Equation.30,Microsoft Equation 3.0Equation Equation.30,Microsoft Equation 3.0Equation Equation.30,Microsoft Equation 3.0AEquation Equation.30,Microsoft Equation 3.07Equation Equation.30,Microsoft Equation 3.08Equation Equation.30,Microsoft Equation 3.0/ 00DTimes New Roman(0(z[ 0 DWingdingsRoman(0(z[ 0  DBrush Script MT(0(z[ 0 B0DSymbolcript MT(0(z[ 0  B . @n?" dd@  @@``_xdtype.wav.WAV 10101RIFFWAVEfmt "V"Vfactdata~|~~}~{~}~|~|~}||~}~~~}{z}~~~~~}~~}~}~~||~}|}~~~|~~}|}}~}~}}~|~}~}~}|~{}~}x{~}{{zz|}}|y{|~{{~pvw~{}}~}z}x}zt~|~{|vy|}}wm}zzrzY_ZmءwSg0.ʻZs_^]ZnJrS+ ՘mnI/pT_ÖUW||{kzaen7J@t_SvupwGqy|oe_]{I^Eb~fUqD`zejtsGswS`{xdiabuq]nskb|};crajwk_gʓinK{]fhmzd]jppngbj~vBn|pyFda~nzqTki~flw{epzvrqvis}NpMalzr~b[QppyUy]bѷ9\vBolyg`|zz~Nh`W{wkumzc{tMwx|u~{|grKha{wwwx~tm{j|smo]nqh[}~mauqu\yyxqz|~}l{zvosykq~{{{t{yt{uopu~f|duog|m}eunvudzsZvwv}gjpzqtuxy{y|xzy}}{{sbrtvql}~vy{`xzyl[xjwxx~oqvr|zut}}uwrx~{gvyqsw{ty{|nsxxwew~}|psw~t|{yxu~{{l{~ltv|{vtu~qo}|wxu{|}}y~xu~vn{|v|z|~y~}n~|uowx}zv{}p{yx~sqrnzwx{z{x{{xx{~{{~~}{|{w~|yzttwxy{}~ww{qrwyzz}yvxuw~}yq~zzu~wz|}|~~~~}}{v~xryw{~}}yyuv}~zqx{{{x~x{~~ts}|z{zwy{}}xt{~z|}zx}vtxku}w{{{}|~x~~~}|||||tw~}~|x{}z|~}y}{y|{~~|{z}}}}|{y~~~~|{y}{z}~|~~zxzzttu}{xw}wtz}zvq||~y{}|zzwz||}{}}|~}~~tz|xvyyvs~|~~}~~}~~{|}y{}x{|z{|zyww{xs}y{~}z{{yx}~z}~|~zx~yz}{y{}}~{z~{xw{}~|y~|}~~~{{}x}~~~~}}~||~yz~}~~~~{y}~}}~{y~~~~}}~}|~~|}}~~~{{|z{|}}~||}|~||~~~~~}~~~{~}|~~~}~}~~~~|}~}}~~~}}x]_s~vmsoowp|~wst}wr~mzus{~ux}vxslvyxxxvum{yw{o~uz}{xsytx{z|u~|vnjjqtvoswq{{ztx~tx~{ysz{|vt||}~~z|~zw~su}}v|~|x~|{~}}}}zy|}}{|}}~}{{|y~y{~~~xv~zzwqt~xrzy|~x|~~wz||~{~{x{z~yxy~}~~}|~~~}x~w}wz~}{x~~|~w~}y~}~~z}~y}{y}~{|}||wz~~|z|xw~~zy}|~~|{|xy~}}}y||~zz|{~yx~}~sszyzx|vsxywspx|sy}rxty{s~}w}}~z||z|}~yx|mj~~uqx~urv|}~x}{}}zyuxx{}z{{|u}}oqvuxkp|s|snpu~y|rkqv|zxyyrp~}xv{x}wxzx||}|wtsz{{wt|}v~~sutt{soztisxpzs{untqw}{{y|yr}~|~xw{}ty}~}z|z|x{~vv{ztjvw~}yt~yu}|lv|vx~{s{w{ww}~{vz|}}wty}|}{}}{xr~~vwz|~}}|~~u{}yv~}|wxs}}z|ww||{{z{|xru{{|~{w{~{~}}||}}{}~zzy{~{}~}~{|}zw|~}z|~z{zz}}{}~zz|~}x{~z~}{~}~~}{{~~|z}{|}}uwxy{y{{y}}~}~yy{{{{x{{z~}~~}{{~zy}~~}~~}~~~||}~{{{||{z|{~~}|~~}}}~{|~|zy}||y}~}}~}}}~~~~~~~}{||~}~~}|}~~}{~|}}}~}}||}~~{zy{{|~|z|~|zz{}|{~~}|}}}}}}|~}~~~}|~~~}~}~~}}~~~~~~~~}~~~}}~~~~~~~}~~}||~~}~}}~}}~}}}}~~~~}~~~~~~}~~}|}~~~~}}~~~~~~~~ LX   )  ^ $ $9Sr$yuIӘqi2$H9Mz1vdiR$FE-Qڛb>"2$iIf/xx 2$fs/fn 2$H9/ecs{ 2$榸ժҴ੆82$\Óu2$@ B%X5da/ F0e0e    A A5% 8c8c     ?1 d0u0@T2 N'p'pA)BCD|E||S" PPf̙@f8FlO ʚ;ʚ;g4KdKd@z[ 0ppp@ <4!d!dl 07<4ddddl 07 <4BdBdl< 0%0___PPT10 pp___PPT9n 8X(4u`ePNG  IHDRF} PLTEfffff3GtRNS@f cmPPJCmp0712Om&IDATc`  @gNS( IENDB`? %          . ` 33333u333ß̙` &L333333x&-LYMMM` ___333___` &L.i~333Ȫn̙}` 7NRLF333đwjg_MMM>?" dd@,? " Ud@ nF $ @`" d n?" dd@   @@``PR    @ ` `p>>   0(  n  VA޽h ?Pergamena &L333333x&-LYMMM___PPT92p22 Carta di riso   E =   (    S t9C?A?Large confetti"1D *"  BFare clic per modificare lo stile del sottotitolo dello schema? ?   6XC "`` C >*   6]C "`  C @*   6aC "`  C @*n  VA޽h ?Pergamena &L333333x&-LYMMM]  08(    0 ,$D  0 lLa probabilit Schema classico2(26$n  VA޽h ?Pergamena ̙337/___PPT10+FD' = @B Dv' = @BA?%,( < +O%,( < +D' =%(DU' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D#' =+4 8?nCB!#ppt_x-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*D' =+4 8?\CB#ppt_hBCB#ppt_hB*Y3>B ppt_h<*+8+0+ + @(  [  BaC̙?",$D  0 MUn fatto qualunque , che non sia certo a priori , si dice aleatorio o casuale>N(29ff  HC?"0p@*,$D  0 G Alcuni esempi(2  HC?"g0x ,$D  0 @ Il lancio di un dado da gioco la durata della degenza in ospedale di un ammalato il numero degli incidenti stradali , nella prossima settimana in un determinato tratto stradale una misurazione scientifica mediante un qualche strumento . qf2fH  0޽h ? &L333333x&-LYMMMxp___PPT10P+D' = @B DG' = @BA?%,( < +O%,( < +D' =%(D' =%(DR' =A@BBB%B0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B%barn(outVertical)*<3<*D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(left)*<3<*D' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(left)*<3<*D' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*S%(D' =-s6Bwipe(left)*<3<*SD' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*S%(D' =-s6Bwipe(left)*<3<*SD' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(left)*<3<*++0+C ++0+C ++0+C +n+   P L (   R  BgC̙?",$D  0 DLe proposizioni che a priori sono incerte si chiamano eventi casuali>E(25ff  HC?"0p@*,$D  0 G Alcuni esempi(2<  HķC?" ,$D  0 6 nella prossima mano di poker verr un poker d assi nel lancio del dado uscir un numero pari la durata della degenza del sig. X sar minore di 20 giorni0 qf2q  BX̙?"  ,$D  0 CUn evento si dice certo quando della sua verit si certi a priori^D(2fff,x  B̙?"  ,$D  0 JUn evento si dice impossibile quando della sua falsit si certi a priori^K(2f ff-4  H@?"p j ,$D  0 zBEsempio: nel lancio del dado otterr un numero non superiore a 14 C(2C8  HT?"@p,$D  0 ~FEsempio: nella ruota di Venezia il primo numero che uscir sar il 100G(2GH  0޽h ? &L333333x&-LYMMMZ R ___PPT102 +ݼD' = @B DI' = @BA?%,( < +O%,( < +D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-s6Bwipe(left)*<3<* D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-s6Bwipe(left)*<3<* D' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<* 4%(D' =-s6Bwipe(left)*<3<* 4D' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<* 4_%(D' =-s6Bwipe(left)*<3<* 4_D' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<* _%(D' =-s6Bwipe(left)*<3<* _D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-s6Bwipe(left)*<3<* D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-s6Bwipe(left)*<3<* D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-s6Bwipe(left)*<3<* D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-s6Bwipe(left)*<3<* ++0+  ++0+  ++0+  ++0+  ++0+  ++0+  ++0+  +d ''`AWpN'(  8l p Tp,$D 0    `?0<Pp,$D 0  p !#  p,$D  02  c $@`,$D 02  c $@,$D 02  c $@p,$D 02  c $ ,$D 02  c $ `,$D 02   c $ p,$D 0l p Sp,$D 0   `?0<Pp,$D 0jt p` *@,$D 02  s *0p,$D 02  s *p`,$D 02  s *0`,$D 02  s *0,$D 02  s *pp,$D 0l 0p Rp0,$D 0    `?0<P0p,$D 0t 0p )`,$D 02  s * 0,$D 02  s *00,$D 02  s * p,$D 02  s *0p,$D 0l P p QpP ,$D 0   `?0<PP p,$D 02  s * ` ,$D 02  s *p`,$D  02  s *,$D  0  00P,$D  0 KGli eventi elementari 2  0pp`W,$D  0 Y!Consideriamo il lancio di un dado" 2" l p p  Ppp ,$D 0   f?0<Pp p ,$D 0 0   (# 0  ,$D 02   s *0  ,$D 02  s *0 ` ,$D  0B + 6DfoP P ,$D   0B , 6DfoP` ,$D   0B - 6DfoP,$D   0B .@ 6DfoP ,$D   0B /@ 6DfoPP,$D   0B 0@ 6DfoP,$D  0 1 0  ,$D  0 IEvento elementare 2f > 0|p` W ,$D  0 WEstraiamo una carta da un mazzo 2  F 0p 00 ,$D  0 G c $` X` ,$D 0 H s *  ,$D  0B I 6Dfo  ,$D  0 J 0 @  ,$D  0 IEvento elementare 2f K 0H 0n,$D  0 3Consideriamo una macchina automatica produttrice di viti: la prossima vite che sar prodotta una delle infinite viti producibili dalla macchina nelle sue condizioni attuali , ognuna delle quali un evento elementare< 2ff  p@  M# p @ ,$D 0   `?0<P p@ ,$D 02   c $  `,$D 0l  p  Wp ,$D  0t  p  L p ,$D 0T ? c $ pp p T @ c $  T A c $  T B c $P T C c $ 0 0 0 T D c $ ` ` ` T E c $  U s * @ 0 ,$D  0 V s * 0 ,$D  0H  0޽h ? &L333333x&-LYMMM<<___PPT10<+BjD;' = @B D:' = @BA?%,( < +O%,( < +D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(left)*<3<*D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(left)*<3<*D ' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*M%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*P%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*Q%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*R%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*S%(D' =%( D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*T%(Dt' =%(D' =%(D3' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*+%(D' =-o6Bwipe(up)*<3<*+D' =%(D3' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*,%(D' =-o6Bwipe(up)*<3<*,D' =%(D3' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*-%(D' =-o6Bwipe(up)*<3<*-D' =%(D3' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*.%(D' =-o6Bwipe(up)*<3<*.D' =%(D3' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*/%(D' =-o6Bwipe(up)*<3<*/D' =%( D3' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*0%(D' =-o6Bwipe(up)*<3<*0D' =%( DR' =A@BBB%B0B%(D' =1:Bvisible*o3>+B#style.visibility<*1%(D' =-6B%barn(outVertical)*<3<*1D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*>%(D' =-s6Bwipe(left)*<3<*>D' =%(D' =%(D3' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*W%(D' =-o6Bwipe(up)*<3<*WD' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*F%(D' =-s6Bwipe(left)*<3<*FD' =%(D3' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*G%(D' =-o6Bbox(out)*<3<*GD' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*H%(D' =-s6Bwipe(left)*<3<*HD' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*I%(D' =-s6Bwipe(left)*<3<*ID' =%( DR' =A@BBB%B0B%(D' =1:Bvisible*o3>+B#style.visibility<*J%(D' =-6B%barn(outVertical)*<3<*JD' =%(D' =%(D@' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*K%(D' =-o6Bwipe(up)*<3<*K+P+0+ ++0+ ++0+1 ++0+> ++0+J ++0+K +L p(  V  BM̙?"`F,$D  0 Definizione : si chiama Spazio Fondamentale di un esperimento C , l insieme dei suoi eventi elementari  2̙fff$f2  NX?"P,$D 0 *   T[?"`L,$D  0 71 3 5   T_?"` 7L,$D  0 72 4 62   H?" ,$D 0%   Hc?" Pb,$D  0 k9asso di cuori asso di fiori asso di denari asso di picche: 2:  Hh?",$D  0 _-2 di cuori 2 di fiori 2 di denari 2 di picche. 2.  Hl?" &,$D   0 T & .. & ... & .. & ..822  Bxg̙?" `P0 ,$D   0 :Definizione : un evento casuale A un sottoinsieme dello spazio fondamentale W~Q(2fff/  H|y?"0P,$D 0 JW,(2ff  H$s?"`@ ` ,$D  0 JW,(2ff6  H?"  ,$D   0 |FA= la faccia che uscir sar pari $ 2$2  T8c?"0 @,$D  02  T8c?"` ,$D  0T  H?"  P ,$D  0 XB= la carta che verr estratta sar un asso &- 2,  B̙?" L,$D  0 <Consideriamo un esperimento C e il corrispondente spazio fondamentale W L insieme E di tutti i sottoinsiemi di W ha le seguenti propriet: W appartiene ad E Se A appartiene ad E anche A appartiene ad E Se A1 , A2 E anche A1 A2 E0 2_ 2) `@pB  NDf?"p P p,$D 0H  0޽h ? &L333333x&-LYMMM+4#4___PPT104+-؍D1' = @B D0' = @BA?%,( < +O%,( < +D' =%(D' =%(DR' =A@BBB%B0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B%barn(outVertical)*<3<*D! ' =%(D' =%(D@' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bbox(out)*<3<*D' =%(D@' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-o6Bwipe(up)*<3<* D' =%(D@' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-o6Bwipe(up)*<3<* D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D ' =%(D' =%(D3' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-o6Bbox(out)*<3<* D' =%(D@' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-o6Bwipe(up)*<3<* D' =%(D@' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bwipe(up)*<3<*D' =%(D@' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bwipe(up)*<3<*D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =%(D' =%(DR' =A@BBB%B0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B%barn(outVertical)*<3<*D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(left)*<3<*D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(left)*<3<*D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*D' =%(D' =%(D@' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bwipe(up)*<3<*D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(++0+ ++0+ ++0+  ++0+  ++0+  ++0+ ++0+ ++0+ ++0+ ++0+ ++0+ ++0+ ++0+ +H VN$(  $ $ Bډ̙?"P,$D  0 JTeorema se A , B E , anche AB E z& 2 f $ B̙?"0,$D  0 NTeorema se A , B E , anche A - B E z( 2 f $ B̙?"p0,$D  0 TDefinizione Due eventi A , B E si dicono incompatibili se AB= C 2 f ff  $ H?"  ,$D  0 PEsempio Si lancia un dado: 22 $ N0?"0  ,$D 0 * $ T?" 9P ,$D  0 71 3 5  $ T?"  ,$D  0 72 4 62  $ T8c?"` P ,$D   02  $ Zp3f8c?"s c ,$D   02  $ T8c?" PP ,$D  0[ $ H` ?"f  ,$D  0 =A e C sono eventi incompatibili A e B sono eventi compatibiliH> 2 ( $ Hh?"&  ,$D   0 n8B-  uscir un multiplo di 3  2( $ Hd?"F ` @,$D   0 n8C- uscir un numero dispari  2$ $ H?" P ,$D   0 j4A-  uscir un numero pari  2  $ H?"  ,$D  0 Sconsideriamo questi eventi:(2H $ 0޽h ? &L333333x&-LYMMM55___PPT105+iD2' = @B D2' = @BA?%,( < +O%,( < +D' =%(D' =%(DR' =A@BBB%B0B%(D' =1:Bvisible*o3>+B#style.visibility<*$%(D' =-6B%barn(outVertical)*<3<*$D' =%(D' =%(DR' =A@BBB%B0B%(D' =1:Bvisible*o3>+B#style.visibility<*$%(D' =-6B%barn(outVertical)*<3<*$D' =%(D' =%(DR' =A@BBB%B0B%(D' =1:Bvisible*o3>+B#style.visibility<*$%(D' =-6B%barn(outVertical)*<3<*$D ' =%(D' =%(D@' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*$%(D' =-o6Bwipe(up)*<3<*$D' =%(D@' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*$%(D' =-o6Bbox(out)*<3<*$D' =%(D@' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*$%(D' =-o6Bwipe(up)*<3<*$D' =%(D@' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* $%(D' =-o6Bwipe(up)*<3<* $D ' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*$%(D' =-s6Bwipe(left)*<3<*$D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*$%(D' =-s6Bwipe(left)*<3<*$D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* $%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<* $D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<* $D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*$%(D' =-s6Bwipe(left)*<3<*$D' =%(D' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<* $%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<* $D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<* $D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*$%(D' =-s6Bwipe(left)*<3<*$D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* $%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<* $D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<* $D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*$ %(D' =-s6Bwipe(left)*<3<*$ D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*$ >%(D' =-s6Bwipe(left)*<3<*$ >++0+$ ++0+$ ++0+$ ++0+$ ++0+$ ++0+$ ++0+ $ ++0+$ ++0+$ ++0+$ ++0+$ ++0+$ +B UM#(((  ( ( BD̙?"`,$D  0 RIl concetto di probabilit(2 (  h0e0e    BCDEFf > 8c8c     ?1 d0u0@T2 N'p'pA)BCD|E|| @S"@0,$D 0l p@P  (@pP,$D 02 ( B?"0@2 ( B?"pP2 ( B?"p2 ( B?"p@l 0P (0P,$D 02  ( H?" P2  ( H?" 2  ( H?"P2  ( H?"0P2 ( H?"02 ( H?" ( H$M?"p *,$D  0 Estraiamo una pallina da un urna contenente 4 palline bianche e 6 palline rosseP 2PE ( H0R?"P ,$D   0 M contiene 10 eventi elementari ciascuno di essi ha probabilit 1/10 di uscita"N W2Nv ( HV?"PP j ,$D   0 hConsideriamo l evento : A: uscir una pallina rossa 85 22 ( H?"@  ,$D 0z p@P ( 0,$D 02 ( B?"0@2 ( B?"pP2 ( B?"p2 ( B?"p@z 0P (  ,$D 02 ( H?" P2 ( H?" 2 ( H?"P2 ( H?"0P2  ( H?"02 !( H?" "( H(`?"p ,$D  0 <W(2" #( T8c?"p,$D   0Y $( HXd?" @ z ,$D   0 GTale evento , unione di 6 eventi equiprobabili , avr probabilit 6/10 H 2H! y '( Bi̙?" `,$D  0 La probabilit di un evento A data dal rapporto tra il numero k dei casi favorevoli al verificarsi di A e il numero degli n casi possibili. 2H ( 0޽h ? &L333333x&-LYMMMD'<'___PPT10'+pSDx%' = @B D3%' = @BA?%,( < +O%,( < +D' =%(D' =%(DR' =A@BBB%B0B%(D' =1:Bvisible*o3>+B#style.visibility<*(%(D' =-6B%barn(outVertical)*<3<*(D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*(%(D' =-s6Bwipe(left)*<3<*(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*(%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* (%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*(%(D' =%(D' =%(D3' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*(%(D' =-o6Bbox(out)*<3<*(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*(%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*(%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*"(%(D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*(N%(D' =-s6Bwipe(left)*<3<*(ND' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*(%(D' =-s6Bwipe(left)*<3<*(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*#(%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*#(D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*#(D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*$(%(D' =-s6Bwipe(left)*<3<*$(D' =%(D' =%(DR' =A@BBB%B0B%(D' =1:Bvisible*o3>+B#style.visibility<*'(%(D' =-6B%barn(outVertical)*<3<*'(++0+( ++0+( ++0+( ++0+( ++0+"( ++0+$( ++0+'( + A ph,(  ,v , B̙?"`` ,$D  0  L evento impossibile ha probabilit P()=0 L evento certo ha probabilit 1 Se A e B sono eventi incompatibili P(A B) = P(A) +P(B)  2J  , H?"0 z,$D 0 >Esempi(2z , HȘ?"`,$D  0 A:  nel lancio del dado otterr un numero non superiore a 14 P(A)=1F 2F , H0?"0,$D  0 B:  nella ruota di Venezia il primo numero che uscir sar il 100 P(B)=0K 2K , H?"pp ,$D  0 Lanciamo un dado e consideriamo: C: uscir un numero maggiore di 4 P(C)=2/6 $P 2!/2 , N?"`  ,$D 0 *l    , ,$D 0 , Tp?" ,$D  0 71 3 5  , T?" ,$D  0 72 4 62  , T8c?"0,$D 02  , T8c?" 0 ,$D  00 , H ?" z,$D   0 v&P(C D)=2/6+2/6=2/34 2P , H?"  ,$D   0 ^D: uscir un numero minore di 3 P(D)=2/60(20H , 0޽h ? &L333333x&-LYMMMC0;0___PPT100+D?.' = @B D-' = @BA?%,( < +O%,( < +D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*,%(D' =-s6Bwipe(left)*<3<*,D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*,-%(D' =-s6Bwipe(left)*<3<*,-D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*,-M%(D' =-s6Bwipe(left)*<3<*,-MD' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*,M%(D' =-s6Bwipe(left)*<3<*,MDA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*,%(D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*,%(D' =-s6Bwipe(left)*<3<*,D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*,%(D' =-s6Bwipe(left)*<3<*,D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*,!%(D' =-s6Bwipe(left)*<3<*,!D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*,!P%(D' =-s6Bwipe(left)*<3<*,!PD' =%(D' =%(D@' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*,%(D' =-o6Bbox(out)*<3<*,D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* ,%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* ,%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<* ,D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<* ,D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*,%(D' =-s6Bwipe(left)*<3<*,D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* ,%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<* ,D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<* ,D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*,%(D' =-s6Bwipe(left)*<3<*,++0+, ++0+, ++0+, ++0+, ++0+, ++0+, ++0+, ++0+, +u J7B7D]06(  0 0 HHڋ̙1?",$D  0 >|Se A e B sono eventi compatibili P(A B) = P(A) +P(B)  P( AB)?(2!  3 0 H?"@p:,$D  0 y9Lanciamo due dadi e consideriamo lo spazio degli eventi: $: 28$l   L0p ,$D  0B  0 TD?" B 0 TD?" B 0 TD?" B 0 TD?" B 0 TD?" B 0 TD?"pp  @  0  K0 0 B 0 TD?" B 0 TD?" B  0 TD?"  B  0 TD?"0 0B  0 TD?"@ @B  0 TD?"P P 0 H|?"0  71,1(2  0 H\?"@ 71,2(2  0 H?"= 71,3(2  0 H?"M 71,4(2  0 H@?"] 71,5(2  0 H?"m 71,6(2  0 H8?"p@ 72,2(2  -0 Ht?"p0  72,1(2  .0 H ?"p= 72,3(2  /0 H?"pM 72,4(2  00 H?"p] 72,5(2  10 H4?"pm 72,6(2  20 H?"pp`  73,1(2  30 H?"p`- 73,2(2  40 H?"p`= 73,3(2  50 Hd"?"p`M 73,4(2  60 H%?"p`] 73,5(2  70 H(?"p`m 73,6(2  80 HH,?"`pP  74,1(2  90 H/?"`P- 74,2(2  :0 H2?"`P= 74,3(2  ;0 H6?"`PM 74,4(2  <0 H9?"`P] 74,5(2  =0 H>?"`Pm 74,6(2  >0 H??"Pp@  75,1(2  ?0 HHA?"P@- 75,2(2  @0 H G?"P@= 75,3(2  A0 HJ?"P@M 75,4(2  B0 HN?"P@] 75,5(2  C0 H\Q?"P@m 75,6(2  D0 HT?"@p0   76,1(2  E0 HW?"@0 - 76,2(2  F0 H@[?"@0 = 76,3(2  G0 H4?"@0 M 76,4(2  H0 Hla?"@0 ] 76,5(2  I0 Hd?"@0 m 76,6(2 2 J0 To?"  ,$D  0 M0 Hh?"P0p,$D 0 <W(2, O0 H(m?"@ ,$D  0 r<A= la somma dei numeri sar 5  22 P0 Ztpo?" ,$D 0 Q0 H q?"6@0,$D  0 A P(A)=4/36 (2 * R0 Hu?"0@ *,$D   0 p:B= il primo numero sar pari  22 U0 T8c?"Pp ,$D  02 V0 T8c?"0P ,$D  02 W0 T8c?"0 ,$D  0 X0 HXz?"PJ,$D   0 @ P(B)=18/36 2 " Y0 Hj?"p@ j ,$D  0 h"AB={(2,3) (4,1)}* 22 Z0 TfԔ?"p@ ,$D 02 [0 TfԔ?"P `  ,$D 0 \0 H̃?"p0j ,$D  0 ^P(AB)=2/36, (2 l ]0 H?" @ p ,$D  0 6P(A B)=4/36+18/36-2/36=5/9` 2H 0 0޽h ? &L333333x&-LYMMM3>+>___PPT10 >+sD;' = @B Dz;' = @BA?%,( < +O%,( < +D' =%(D' =%(DR' =A@BBB%B0B%(D' =1:Bvisible*o3>+B#style.visibility<*0%(D' =-6B%barn(outVertical)*<3<*0D ' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*0%(D' =-s6Bwipe(left)*<3<*0D' =%(D3' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*L0%(D' =-o6Bwipe(up)*<3<*L0D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*J0%(D' =-s6Bwipe(left)*<3<*J0D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*M0%(D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*O0%(D' =-s6Bwipe(left)*<3<*O0D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*P0%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*P0D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*P0D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*Q0%(D' =-s6Bwipe(left)*<3<*Q0DN' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*R0%(D' =-s6Bwipe(left)*<3<*R0D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*W0%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*W0D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*W0D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*V0%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*V0D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*V0D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*U0%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*U0D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*U0D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*X0%(D' =-s6Bwipe(left)*<3<*X0D0 ' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*Y0%(D' =-s6Bwipe(left)*<3<*Y0D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*Z0%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*Z0D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*Z0D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*[0%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*[0D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*[0D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*\0%(D' =-s6Bwipe(left)*<3<*\0D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*]0%(D' =-s6Bwipe(left)*<3<*]0+0+0+0 ++0+0 ++0+M0 ++0+O0 ++0+Q0 ++0+R0 ++0+X0 ++0+Y0 ++0+\0 ++0+]0 +a #4(  42 4 N0?"`  ,$D  0 *2 4 Nf8c?"  ,$D  02 4 N?"`,$D 0 *  4 HH̙1?"`b,$D  0 RProbabilit condizionate(2V 4 Hh?"0,$D  0 dB: lanciando un dado uscir un numero minore di 4 3 23X  4 Hď?",$D  0 \A: lanciando un dado uscir un numero dispari &/ 2.2  4 T8c?"@,$D  0 4 Hɏ?"pj,$D   0 JP(A)=1/2 P(B)=1/2 2h 4 H͏?"z,$D   0 xSupponiamo di sapere che si verificato A e di voler valutare la probabilit di B , data questa ulteriore informazione.y 2yB 4 Hҏ?"pj ,$D   0 @La indichiamo con P(B/A) e la chiamiamo probabilit condizionata,A 2(f 4 H`׏?"  ,$D   0 W! cambiato lo spazio degli eventi" 2" 4 T`ۏ?"  ,$D  0 71 3 5 4 HLߏ?" p  ,$D  0 D P(B/A)=2/3 (2  4 0A  ?̙?@ 8  $D  0 4 0A 2?̙?p 5 8 2$D  02 4 Z2OAPP8c?"p,$D  0 4 H?"` ,$D  0 YConsideriamo gli eventi :$ 2  4 H0?"@ ,$D  0 Cda cui si ricava: 2 !4 0A ?̙? 08 $D  0z   4 @,,$D 0 4 T?" ,$D  0 71 3 5 4 T?" ,$D  0 72 4 6 "4  `A 7??" p 8 7$D  0 #4  `A 8??"p  7 8 8$D  0H 4 0޽h ? &L333333x&-LYMMMHH___PPT10H+DE' = @B DoE' = @BA?%,( < +O%,( < +D' =%(D' =%(DR' =A@BBB%B0B%(D' =1:Bvisible*o3>+B#style.visibility<*4%(D' =-6B%barn(outVertical)*<3<*4D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*4%(D' =-s6Bwipe(left)*<3<*4D ' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* 4%(D' =-s6Bwipe(left)*<3<* 4D' =%(D@' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*4%(D' =-o6Bbox(out)*<3<*4D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*4%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* 4%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<* 4D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<* 4D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*4%(D' =-s6Bwipe(left)*<3<*4D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*4%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*4D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*4D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*4%(D' =-s6Bwipe(left)*<3<*4D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*4%(D' =-s6Bwipe(left)*<3<*4D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*4%(D' =-s6Bwipe(left)*<3<*4D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*4%(D' =-s6Bwipe(left)*<3<*4D' =%(D' =%(D@' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*4%(D' =-o6Bbox(out)*<3<*4D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*4%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*4D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*4D' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*4%(D' =-s6Bwipe(left)*<3<*4D' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*"4%(D' =-s6Bwipe(left)*<3<*"4D' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*#4%(D' =-s6Bwipe(left)*<3<*#4D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*4%(D' =-s6Bwipe(left)*<3<*4D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*4%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*4D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*4D' =%(D' =%(DE' =4@BBB%B%(D' =1:Bvisible*o3>+B#style.visibility<*4%(D' =-6B%barn(outVertical)*<3<*4D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* 4%(D' =-s6Bwipe(left)*<3<* 4D' =%(D' =%(DE' =4@BBB%B%(D' =1:Bvisible*o3>+B#style.visibility<*!4%(D' =-6B%barn(outVertical)*<3<*!4++0+4 ++0+4 ++0+4 ++0+4 ++0+ 4 ++0+4 ++0+4 ++0+4 ++0+4 ++0+4 ++0+4 ++0+4 ++0+ 4 +[ 8(  8 8 H'̙1?"`P0b,$D  0 WEventi indipendenti((2 8 HX.̙1?" ,$D  0 DDefinizione: due eventi A e B sono tra loro indipendenti se P(AB)=P(B)P(A)^f 2. f * 8 H4?"p *,$D  0 pIn generale P(B)P(B/A) , se dovesse verificarsi che : P(B)=P(B/A) allora gli eventi A e B sarebbero tra loro indipendenti ^| 2'3f 8 H<?"  ,$D 0 >Esempio: 2 2 8 NA?"PP  ,$D 0 *z   8  ,$D 0 8 T7?" ,$D  0 71 3 5  8 TH?" ,$D  0 72 4 6&  8 HL?"p  j ,$D  0 l,Lanciamo un dado e consideriamo gli eventi: $- 2+&  8 H@R?"  ,$D   0 lA= {1,2,3,4}8 2 2  8 T8c?"`` ,$D   0 8 H X?"  ,$D   0 \B= {4,5,6}* 2  8 H\?" p ,$D   0 JC={2,4,6} 2 2 8 ZIS8c?"  ,$D   02 8 T8c?" ,$D  0 8 HDa?" @ ,$D  0 P(A)=4/6 P(B)=3/6 P(C)=3/6 P(A B)=1/6 P(A)P(B) P(A C)=2/6=P(A)P(C) HI 2!B 8 ZDfԔ?"` ` ,$D  0 8 H0h?" ` P ,$D  0 [A e B sono dipendenti*(2  fB 8 ZDfԔ?" ,$D  0 8 Ho?"  ,$D  0 ]A e C sono indipendenti*(2  f 8 Zr?"P (p,$D 0 :WH 8 0޽h ? &L333333x&-LYMMMBB___PPT10B+ yoD?' = @B DK?' = @BA?%,( < +O%,( < +D' =%(D' =%(DR' =A@BBB%B0B%(D' =1:Bvisible*o3>+B#style.visibility<*8%(D' =-6B%barn(outVertical)*<3<*8D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*8%(D' =-s6Bwipe(left)*<3<*8D' =%(D' =%(DR' =A@BBB%B0B%(D' =1:Bvisible*o3>+B#style.visibility<*8%(D' =-6B%barn(outVertical)*<3<*8DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*8%(D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* 8%(D' =-s6Bwipe(left)*<3<* 8D' =%(D' =%(D@' =A@BBB B0B%(D' =1:Bvisible*o3>+B#style.visibility<*8%(D' =-o6Bbox(out)*<3<*8D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*8%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*8%(D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* 8%(D' =-s6Bwipe(left)*<3<* 8D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* 8%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<* 8D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<* 8D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*8%(D' =-s6Bwipe(left)*<3<*8D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*8%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*8D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*8D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*8%(D' =-s6Bwipe(left)*<3<*8D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*8%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*8D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*8D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*8%(D' =-s6Bwipe(left)*<3<*8D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*83%(D' =-s6Bwipe(left)*<3<*83D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*83I%(D' =-s6Bwipe(left)*<3<*83ID' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*8%(D' =-s6Bwipe(left)*<3<*8D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*8%(D' =-s6Bwipe(left)*<3<*8D' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*8%(D' =-s6Bwipe(left)*<3<*8D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*8%(D' =-s6Bwipe(left)*<3<*8++0+8 ++0+8 ++0+8 ++0+8 ++0+8 ++0+ 8 ++0+ 8 ++0+8 ++0+8 ++0+8 ++0+8 ++0+8 ++0+8 +~ 6B.BLRD0 A(  Db :D T|?" ,$D  0b ;D T|?" ,$D   0" ?D T|?",$D   0$z   D  ` ,$D  0B D TD?" B D TD?" B D TD?" B D TD?" B D TD?" B D TD?"pp  N  0   D  0 B  D TD?" B  D TD?" B  D TD?"  B  D TD?"0 0B D TD?"@ @B D TD?"P P D H ?"0  71,1(2  D HP?"@ 71,2(2  D H?"= 71,3(2  D H ?"M 71,4(2  D Hd?"] 71,5(2  D H?"m 71,6(2  D H?"p@ 72,2(2  D HH?"p0  72,1(2  D HÖ?"p= 72,3(2  D HƖ?"pM 72,4(2  D H,ʖ?"p] 72,5(2  D Hx͖?"pm 72,6(2  D HЖ?"pp`  73,1(2  D HԖ?"p`- 73,2(2  D H\ז?"p`= 73,3(2  D Hږ?"p`M 73,4(2   D Hݖ?"p`] 73,5(2  !D H@?"p`m 73,6(2  "D H?"`pP  74,1(2  #D H?"`P- 74,2(2  $D H$?"`P= 74,3(2  %D Hp?"`PM 74,4(2  &D H?"`P] 74,5(2  'D H?"`Pm 74,6(2  (D HT?"Pp@  75,1(2  )D H?"P@- 75,2(2  *D H?"P@= 75,3(2  +D H?"P@M 75,4(2  ,D H?"P@] 75,5(2  -D HD ?"P@m 75,6(2  .D H?"@p0   76,1(2  /D H8?"@0 - 76,2(2  0D H?"@0 = 76,3(2  1D H?"@0 M 76,4(2  2D H?"@0 ] 76,5(2  3D Hh?"@0 m 76,6(2 2 4D To?"  ,$D  0 5D H"?"0,$D 0 <W(2 6D HP'?",$D  0 HLanciamo due dadi 2  7D H*?",$D  0 Pconsideriamo i due eventi: 2x 8D Hh.?"0p *,$D  0 LB1 =  la somma minore o uguale a 7 V' 2  D HE?"P ,$D   0 v0A=  il primo numero 2 * 2 @D H+B#style.visibility<*6D%(D' =-s6Bwipe(left)*<3<*6DD' =%(D' =%(D3' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*D%(D' =-o6Bwipe(up)*<3<*DD' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*4D%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*4DD' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*4DD' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*5D%(D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*7D%(D' =-s6Bwipe(left)*<3<*7DD' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*8D'%(D' =-s6Bwipe(left)*<3<*8D'D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*:D%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*:DD' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*:DD' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*LD%(D' =-s6Bwipe(left)*<3<*LDD' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*;D%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*;DD' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*;DD' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*+B#style.visibility<*=D%(D' =-s6Bwipe(left)*<3<*=DD' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*>D%(D' =-s6Bwipe(left)*<3<*>DD' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*?D%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*?DD' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*?DD' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*@D%(D' =-s6Bwipe(left)*<3<*@DD' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*ND%(D' =-s6Bwipe(left)*<3<*NDD' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*RD%(D' =-s6Bwipe(left)*<3<*RDD' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*QD%(D' =-s6Bwipe(left)*<3<*QDD' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*KD%(D' =-s6Bwipe(left)*<3<*KD++0+5D ++0+6D ++0+7D ++0+8D ++0+D ++0+@D ++0+LD +a &&08@@&(  @" 6@ T|?"0  ,$D 0. @ HЬ?"`Z,$D  0 t2Consideriamo due urne dalle seguenti composizioni:&3(213 @  p0e0e    B0CpDEF Ԕ 8c8c     ?1 d0u0@T2 N'p'pA)BCD|E||p0p000 @S" ,$D  0 @  v0e0e    B0CpDEF Ԕ 8c8c     ?1 d0u0@T2 N'p'pA)BCD|E||p0p000 @S" ,$D  0 @ H?"F`@,$D 0 XB1:(2333 @ H?"F @,$D 0 XB2:(2 @ Hh?"p: ,$D  0 VSi sceglie una pallina da un urna a caso. La pallina bianca (evento A) Qual la probabilit che la pallina provenga dalla prima urna? &(22 @ To?" P ,$D  0l pP @ 8@P p@,$D  02  @ TEf?"02 @ NE?"P  2 @ NE?"PP  2 @ TEf?"@2 @ TEf?"p2 @ TEf?"l 0 @0 ,$D  02  @ H?"@P2  @ H?"P2  @ H?"PP2  @ H?"P2 @ N̙?"`P2 @ N̙?" P2 @ H̙?"pP2 @ H̙?"0Pl    7@  ,$D   02 @ H?"0  2  @ H?"P0  2 !@ H?"0  2 "@ H?"0 ` 2 #@ N̙?"0p  2 $@ N̙?"p  2 %@ N̙?"p @ 2 &@ N̙?" @ z  P '@  ,$D  02 (@ Hf?"P2 )@ B?"@P2 *@ B?" P2 +@ Hf?" pP2 ,@ Hf?"PP2 -@ Hf?"0PB .@ TDo?" P ,$D   0 /@ Ht͗?" @ ,$D  0 <W(2 0@ Hї?"  ,$D  0 XB1:(2333 1@ HL֗?" @,$D 0 XB2:(2z  0 2@ @  ,$D  0 3@ <4ܗ?" 0 H (1/2)(4/8) P(B1 /A)= = 3/5 (1/2)(4/8)+(1/2)(2/6) R 2! s%B 4@ TDo?":H @ 0޽h ? &L333333x&-LYMMM::___PPT10:+cD9' = @B D8' = @BA?%,( < +O%,( < +D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*@%(D' =-s6Bwipe(left)*<3<*@D' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*@%(D' =-s6Bwipe(down)*<3<*@D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*@%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*@D' =+4 8?dCB0-#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*@D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*@%(D' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*@%(D' =-s6Bwipe(down)*<3<*@D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*'@%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*'@D' =+4 8?dCB0-#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*'@D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*@%(D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*@*%(D' =-s6Bwipe(left)*<3<*@*D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*@*I%(D' =-s6Bwipe(left)*<3<*@*ID' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*@I%(D' =-s6Bwipe(left)*<3<*@ID_' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*@%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*@D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*@D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*/@%(Do' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*7@%(D' =-s6Bwipe(down)*<3<*7@D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*0@%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*.@%(D' =-s6Bwipe(left)*<3<*.@D' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*8@%(D' =-s6Bwipe(down)*<3<*8@D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*1@%(Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*6@%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*6@D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*6@D' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*2@%(D' =-s6Bwipe(left)*<3<*2@++0+@ ++0+@ ++0+@ ++0+@ ++0+/@ ++0+0@ ++0+1@ +!P #<(  <) < H\̙1?"VpX,$D  0 oLa formula di Bayes(2T < HT ?"0,$D  0 Consideriamo n eventi incompatibili B1 , B2 , . . . ,Bn tali che Bi= WK 2%   < Z(?" ,$D 0 :WP < H?"@ P,$D  0 :sia A un altro elemento di W @(22 < N?"0` ,$D 0l `0  <`0 ,$D  0B  <B ZDԔ?"P`B < ZDԔ?"B < ZDԔ?"PB < ZDԔ?" p < Nl$?"`60 JB1,(2 < N)?"Pp JB2,(2 < N,?"60 0 dBn,(22 < ZԔ?"` p,$D 0 < N1?",$D 0 ;A(2f < H5?"g,$D   0 V A=AW=. 2p < H`=?"y` ,$D   0 lP(A) = P (A B1 ) + P (A B2 ) + . . .+ P (A Bn )=.7 2  < 0A ?̙? [ 8 $D  0 < HM?"i P ,$D   0 9C= P (B1) P (A/ B1 ) + P (B2) P (A/ B2 ) +. . . + P (Bn) P (A/ Bn ) D 2   < Hb?"` g,$D   0 .A(B1 B2 . . . Bn )= 2  !< Htj?" p,$D   0 J(A B1) (A B2) . . . (A Bn)& 2  "< ZA A??" @ 8 A$D  0 #< T̙Ԕ?"  ,$D  0H < 0޽h ? &L333333x&-LYMMM44___PPT104+sD82' = @B D1' = @BA?%,( < +O%,( < +D' =%(D' =%(DR' =A@BBB%B0B%(D' =1:Bvisible*o3>+B#style.visibility<*<%(D' =-6B%barn(outVertical)*<3<*<D ' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*<%(D' =-s6Bwipe(left)*<3<*<D' =%(D3' =4@BBB B%(D' =1:Bvisible*o3>+B#style.visibility<*<%(D' =-o6Bbox(out)*<3<*<D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*<%(D' =-s6Bwipe(left)*<3<*<D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*<%(D ' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*<%(D' =-s6Bwipe(left)*<3<*<D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*<%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*<D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*<D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*<%(D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*<%(D' =-s6Bwipe(left)*<3<*<D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* <%(D' =-s6Bwipe(left)*<3<* <D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*!<%(D' =-s6Bwipe(left)*<3<*!<D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*<7%(D' =-s6Bwipe(left)*<3<*<7D' =%(D' =%(DD' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*<%(D' =-s6Bwipe(left)*<3<*<D' =%(D' =%(DE' =4@BBB%B%(D' =1:Bvisible*o3>+B#style.visibility<*<%(D' =-6B%barn(outVertical)*<3<*<D ' =%(D' =%(DE' =4@BBB%B%(D' =1:Bvisible*o3>+B#style.visibility<*"<%(D' =-6B%barn(outVertical)*<3<*"<D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*#<%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*#<D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*#<D' =+4 8?RCB?BCB#ppt_xB*Y3>B ppt_x<*#<D' =+4 8?RCB?BCB#ppt_yB*Y3>B ppt_y<*#<+0+0+< ++0+< ++0+< ++0+< ++0+< ++0+< ++0+< ++0+< ++0+ < ++0+!< +!xVOSA}-(!&p0p9b6`!EkhТ^&+Q`Co^N$^ě4{>߁Zi¼L;;ݙ{{@Z_|_2OgO]zFPrU; C1@9܊܆y@h=i9ki=oUjp K3N /? οYO~v/Џa$wSR*RS8g]g3]_ T1֙GPA&F,t0.ޘ--a3issjKN3ܜ0gçKYczu AO{L14>4vo1O;W'E6"jWB$TLtJ4*-fs9mN[t/35 h%Q}GcJuטގٳ[) j8 wg(g%w-[gj: h94f)w K&JyBʂ1,YN$c@ E?u'_+-W͹A0D-ȭHoSW=otJXȔT)[Jgfm^? O=_Oy~f s\QF'(;"=CɖZ _tqːftD:vQy;x5Fq4 &(*(=EQ꼡1QNKX*OuN|b|a$:OXG1N\BdEjOzAUur%LR;JU=ghҠ f+Jh#u]|s>%'dmOE;ir<{v,3_j&}g"ӳ򝐼>?lZd0 u[ݞj(@@]OKgJrt'S#{@ٯ>Z>ea݄J{)-ĈiE]6;GvLh~\uti%/pfS1h`HZ!ħHsrO(xӸ|&Moz0<Zcyy9e;}-bcbW^{bfTX- ŭT9[Jf. d^ ?7t3 ka$k/tb"#Tɖz(=9S>޲a;*(z\EyC:~XLT6]yzN‰O0Yɥ x=5fʡ c\iL_ u.1&2>κ~%˔M}KvFfޔ/H6;Ac\&9av^xm 8[;Hs|EKQ)N@a`~dTXH)a8|j.⢭11/ DPmvd2T)6s~{}¢ E؂x=pII7t=yf+)ߦ^"4WxVMLSA}x-Ж 1pI`C9xVKڢ*Fr0H0&xࡉWOZgvK bTefvgٙnt}R#xl}L7I~bT*wh_66:ˁΣ`W)EeA Ǝd L))`5ak2Y? \?tOnIV\ƝC:F ֔)451[fl- @+=y:HSo( S垳)&3lz6g/,Fstt.RUwKl+=D =dfr2Q-U10Ȟ>){Npl3ug(zZKWC unH<u#͟<}J>^Ƀ?$q*yD5pD2&7t2[3=3ff"Hky]ǷXHU!Ӯoz] +r-e<)ĹGфWK@ݧNN3OL[KLc^ܛLt$yw$œU pKeRd>hyv.C fr;d@`&zKi[\)`Efսj*9.4 Q|%wखnzY>qg=kn]R3/0%[xXMlE~3k:M;4?)N".UҒBR!U%jPm|A4E.\9Hd D}Nڼ73,VT"zf{ߛ7uT%j}LWZݵ=y.>>Qi'O"X0yn@}Wzb<7/y5;OY?S m)&p朏W` X#?4'dN",l´y>5_n@j: vGDn{yO@5@DBFAPGA>:G=Pc{?+d{jK¹5~1S\-#iQJ,} y~uoKDj,{ky#@cXWUTR S]L=cѓd}'ř_?ua}el}F( 0l:Txti iFGuqp/\ʭ.''܁i6F0^rʟH+|@+|o;Pkg&[Ϥ$?pY$cPgъ`N**Ui{]^e7R!%pWއg'oOxgp?Gtuᔍ>'ulJ,3ϙWv})9n&'ol{ uB\??.Wض??8iN K6z>}gx?F|G| _nާ1xK~=[N {~i_a|*l}O=̧~/{W#arU64<;q׷0F6JG+ A'>'riePLﮪ?^{$X:)c3,|y% 8F o;ww&@goMT߭L5|@~eL{no%6 _?n"doXq |.{giߖG_+ؓx;lQ%!5PUH JPH ( CZBiR s%`eNHH],0ll( L ޅ멐"'l?~g㇡ӗc_Af^)`p7[-n G}C^E78HA *"סci< y]._vƯ\7L#ZgUX'Ng|%̿k OK*kxT &aTb,?uf!D?C(}Cп5g`XZ@֞|~qT)-UDy#W͗d4&Ji6ݖ$|ܝK+Z;c洆iUtP%[b0I gJ;mRaSGPG9 }C:!Uofjk8bF0.f's xVkSQ4I>cRɡHZPb md@͇&*$qPpC]`'usms(1[m~ýs=|%Ŕ>n/XhMҰ2|˽v~1u EL,G;XB&E[hAK?w׷sa܅RY~Ou0܅܄_I I(~⹉~QbϯqE+O1]1󮉛/e?gJ@| } ex_,'WN${Iq%ջi -*gdE++'Ԥ^9EH.EעDgb0e*` 1sq[IRҪsQ9Jy'}X''hrzvgyd_j{"{eRn8RR=-JWlyloG Kkû*wo!w(U*Uux[ug7i/걶x1xXaKw 4ҝyl&Y`>ۿb^јBXic|r,W߻k4#jW8ǣmLo}=v~'rp"'3V?=Z7f_rOz4g]j0qm `zpsBz6?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstvwxyz{|~Root EntrydO)PicturesWCurrent User}SummaryInformation(J