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mode 100644 index 0000000..ed29a07 --- /dev/null +++ b/3e/Gestion_donnees/Probabilites/exos_proba.tex @@ -0,0 +1,127 @@ +\documentclass[a4paper,10pt, twocolumn, landscape]{article} +\usepackage{myXsim} + +\title{Probabilités - Exercices} +\tribe{Troisième} +\date{Septembre 2017} + +\thispagestyle{empty} +\geometry{left=5mm,right=5mm, bottom= 10mm, top=10mm} + + +\begin{document} + +\begin{exercise}[subtitle={\Rep\Com}] + On lance un dé équilibré à 6 faces et on regarde le nombre inscrit sur la face supérieur. + + Calculer la probabilité chacun des évènements suivants + + \begin{center} + $A = \left\{ \mbox{ On obtient 4 } \right\}$ \\ + $B = \left\{ \mbox{ On obtient 3 ou 5 } \right\}$ \\ + $C = \left\{ \mbox{ On obtient un nombre impaire } \right\}$ \\ + $D = \left\{ \mbox{ On obtient un nombre négatif } \right\}$ \\ + $E = \left\{ \mbox{ On obtient un nombre inférieur ou égal à 4 } \right\}$ + \end{center} +\end{exercise} + +\begin{exercise}[subtitle={\Rep\Com}] + On place dans un chapeau 10 papiers sur lesquels sont inscrit les chiffres nombres de 0 à 9. On tire un papier au hasard et on observe le résultat obtenu. + + \begin{enumerate} + \item Préciser toutes les issues possibles de cette expérience aléatoire. + \item Quelle est la probabilité de tirer un papier avec le chiffre 0? + \item Quelle est la probabilité de tirer un papier avec un chiffre plus petit que 4? + \item Quelle est la probabilité de tirer un papier avec un chiffre plus petit que 10? + \item Quelle est la probabilité de tirer un papier avec un chiffre plus grand que 20? + \end{enumerate} +\end{exercise} + +\begin{exercise}[subtitle={\Rep\Com}] + On place dans une urne les boules, indiscernables au touché, suivantes + + \includegraphics[scale=0.2]{./fig/boules} + + On tire une boule au hasard. + + \begin{enumerate} + \item On s'intéresse à la lettre inscrite sur la boule. + \begin{enumerate} + \item Quelles sont les issues possibles de cette expérience? + \item Calculer la probabilité de tirer une boule avec un A dessus. + \item Calculer la probabilité de tirer une voyelle. + \end{enumerate} + + \item On s'intéresse à la couleur de la boule. + \begin{enumerate} + \item Quelles sont les issues possibles de cette expérience? + \item Quelle est la probabilité de tirer une boule blanche? + \end{enumerate} + + \end{enumerate} +\end{exercise} + +\begin{exercise}[subtitle={\Rep\Rai}] + \begin{enumerate} + \item Alice participe à un jeu télévisé. Elle a devant elle trois portes fermés. Derrière l'une d'elle, il y a une voiture et derrière les autres, il n'y a rien. Elle doit choisir une de ces portes pour remporter la voiture. Quelle est la probabilité qu'elle gagne une voiture? + \item S'il y a quatre portes au lieu de trois mais toujours qu'une seule voiture. La probabilité qu'Alice gagne la voiture augmente-t-elle? + \end{enumerate} +\end{exercise} + +\begin{exercise}[subtitle={\Rep\Rai}] + % Équiprobabilité, pourcentage + La tableau suivant indique les quantités de poissons d'un étang ayant certaines caractéristiques. + \begin{center} + \begin{tabular}{|*{5}{c|}} + \hline + & nageoires & ailerons & pattes & total \\ + \hline + bleu & 54 & & 30 & \\ + \hline + vert & & & 34 & 104 \\ + \hline + total & 74 & 60 & & \\ + \hline + \end{tabular} + \begin{enumerate} + \item Compléter le tableau. + \item Les poissons ont autant de chance de se faire pêcher. Donner la probabilité des événements suivant arrondis à un chiffre après la virgule. + + $A = \left\{ \mbox{ le poisson est bleu } \right\} $ \\ + $B = \left\{ \mbox{ le poisson a des pattes } \right\} $ (étrange ce type de poissons!) \\ + $C = \left\{ \mbox{ le poisson a des ailerons vert } \right\} $ \\ + $D = \left\{ \mbox{ le poisson est rouge } \right\} $ \\ + \item Si on pêche uniquement les poissons à nageoires, quelle est la probabilité d'attraper un poisson vert? + \end{enumerate} + \end{center} +\end{exercise} + +\begin{exercise}[subtitle={\Rai\Com}] + Devant Bob, il y a deux boites avec des bonbons tous emballés de la même façon. + + Dans la première, il y a 10 bonbons à la menthe et 14 bonbons à la fraise. + + Dans l'autre, il y a 14 bonbons à la menthe et 18 bonbons à l'abricot. Bob ne peut piocher qu'une seule fois un bonbon. Il préfère les bonbons à la menthe. + + Dans quelle boite doit-il piocher son bonbon pour avoir le plus de chance d'avoir son goût préféré? Expliquer. +\end{exercise} + +\begin{exercise} + Sur les faces d'un dé à 8 faces sont écrites les 8 lettres A, B, C, D, E, F, G, H. On lance le dé et on observe le résultat obtenu. + + \begin{enumerate} + \item Préciser toutes les issues possibles de cette expérience aléatoire. + \item Proposer un évènement non élémentaire. + \item Proposer un évènement impossible. + \end{enumerate} +\end{exercise} + + +\end{document} + + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: "master" +%%% End: + diff --git a/3e/Gestion_donnees/Probabilites/fig/boules.pdf b/3e/Gestion_donnees/Probabilites/fig/boules.pdf new file mode 100644 index 0000000000000000000000000000000000000000..86d93d1e1443e0bffc0d86205d83da83888c595d GIT binary patch literal 11850 zcmd^F2|ShS)^AcsgQAS}Mr5|n zh>)R@smPQJ-}~;366cm1U+-$wY!3 zvrFvd%QYd~DlAG9GwencL7iU?E8UHBo>u=|EY@nL1?xf6wd>cHJ_(xq>Y33f&g8Fh zbi=ykhA~zJw)PH)lvtWj6bn3*^ZN}#l-U+?qq|&mHzS}Mz;U{t>T(yzA z1h>hS+&p%quG1@j#)TiNpnmRRjh5sI9$87!X2ar+j>8`l=Z3%Pd&o+9&nlHE%!ys_ zO5X6~S(^O^B|QTp3P)R;WaNdEU?YRZPw}_HboX0#UkdsDw2@0#eT45pkB^O5-h}+= zp3FOL5)HoW{o=>Y>7blBd+gul-0(FV{g$_5iwAcpK^?<&_mxn*%DpFO^J{%#$b5#f zMxo2C1;X_lU-s_DoX}`Grcv3)JL4EIp<-nBu2-k1i@7-gdt0|aN*xmysk|w9=AB`=F`*hhk!kbLdyaMY{mh7zUb54!& zG{n`{guvKx>S9uAU%N^b9mud5>uu^Sa$hgw*WR_WUAK3;<4C;O<85uj(T@UgvrGxm z&%*6TpV_A5)FBf;t9m7+Ss3Nl)+up^nV2m8rMsk|!UnsnXK5%9`cNx!GtuCys&zjcZ zakp)XZ8$Ym@35gY=OfKB4jeXqH0yq~#1g58&tD;BWwZ=u|io z03YamzO^#R9%{NUr<39^aTtJwYCt5g68Ow77rwv+Xhla{9f*LWHo=kz)dOG1M6e^; zFf_s;qJ=dVRG{+$-~L}i#cu-0$X zOhR!xgW`6XwdRTx4St4==37P7^;EmptjhLej9!i{Xv6+Fzp?)>_`Os~(7C-7;BX88 zKJx(nMGB%lh$FC73R`cUO0={-Nw6@z78+ZVl3YH};_1i>oxU05x96~n6BgN&og zAdO0`ar|OgBmY2$3|T==^LwFGur=ko;i- z|Fts`vD_;EH$oDJ13ivKNa8W*{{TpWW;Nt$ffg(H2C785)lb*Xi>mn-i*@5h{uLpa z&&&9F`97ezQ2%R?{Ey@LUw|YUK+tT)d5`jM9Fi943y?gtlGTb>?mqk>BC!H=RZws3sCda%BQ@l1J3pq~*zzS*p;tOJ{)%Gl{(lE1kkJ^{H) zj`L%yoR@pW^+%+~QSG0HXIBeWG&wx%V$RRlHO_jNC+b>wI-B5Lv%E)v3j3bijNB9a zntEQxz>J+;6lL|I%!k?Rgo9wUk9ye2$JKeEn(+Y^BUdtw59Zq#DlqJdE99-?GQY}M zr8c;~V#rxfEPo&Mfx)Al22n$&(LF#|vN7}4=Te2Tw+dOPB6}wKCm1Uj_ZYm+Wg7pszx$h^L$S$dn%1YxsvZ*!2j}yJGKqt5ROmC?$vr|?b>z%v;#Y|H^ zWt|FN0gY1sW6C-0?-ay6@pdfNb7~Y05{|n0SPqQyL@?g6xXSm?O#F@@<+W3J$TNS= z2!7*!6Bfl!g%aV{n0610&Gbq*QYD=pZ`2%Ym|Yz>fW5O^gfw<8h!Brh6yXof|7#+o zo&3LG54jjJ`*(=zM2=o^?2{jh;2{LtMPJG*tIUAE;4@eY8I zqevO9Nvjqaf7ctx zHg*2Fb8^J+RBPeM0B(`TRa22KZf5K`d$(Nt!68$TqM=9=DS`dg#NyuTOf1xv1T8 znYhv5>-+8SB>2O+{nsRjTuFjI z4$(i7AYImQ0EI-smgvC2qnoHl8gtt}dQChdog`Z#n0%*UdwAIt6%I~rOyuPgk;|0a z+F;7f1oMwjXG)w#DgRa@hv7TPwod7uG`C->u%FPqTy`Z@b3?UTI)*_CH|-MdrC6P_ zNOKqbt+4(0pc^Uk!D~ZOW;~@fHfKWi<9>JV(+S8ZHr9MA0iQFJ54Gtsbw$Y`s-O80 zLsxTpiUCjI4BsjOt8i9U+dkgWddzTUoG zk%PnUCl&C;u{PlaJNc8pqf`dlwdU?sVGh7<;Ub43E(Lk9?b4D}O2uqSc%3?u|Bf#~ z{`Z=pSE=Gz)TwvmC!12%xhI#2q&Z6sV7B}7r8(zkhCH58&q^b7YdTTCX)vcn=r@ad zzLu!H{GtwfZ>j>hK6hPsL^?~9V1@<%oA?3MROaIfx%UEMo!`T39j;o7wB;%4aS+ug zdKc~-6o>D6#7DX58Eu|<-162zxBBM58*j41MB+qL*fWfJfF|6NkHK4;;xOv%CQV3+ zaoYI!b#s!KR^~fBh2*62qTQcPjk>C*UFuvNZ&~DSd_i_hY!J=;-EQ2D%T#MZoA8Ls z)af*Pd9}3DwSI*tr=hO=GS6zxwMZ7dn>rhh*oS)Tc+Yl$=W<_>$n{UB(rcv~G(1cU z0(VL2%6uMZa@pdomwEX8sTX~3;*g&|@J~yWRH_WcyLxmT7z+-oYCt{^oR(6zu#Y(1 zm3qb@J+ltQWqmoh?rnGdQ)?B$Xf?+usm;50#20RpWxvld$`~Mwzc~{Bz2z`!f&~^b z8o`m^+;L-n%w%M0{KczTT_2f?!~K0{qK2Q#Y|h;FE=%?c&UrWW?)Tl-C>Oi3;*Tfa zO8a(<$H`2$_J*jDJ)1<%jlDd3r8{giS#vSA5?zH!~d*_b}+QK6hi=Md9yfT81uo zgw&?9y`LM|7-#c!D4zZOgN#g@;;FzEso}_k+FM-@CM~BiCG26%m(CYyn4J#2c!sKr z!^UwLzfhhNY3yx5zWnISA^d4A+7UPp695HiJGd9#7uU70OARwTRmt;M;o(cJM z--`e-zpLQ=5uXaumv0&} zCFqdxY4Tvjp^OVQ#g3&(ez}DwX2z$CeN0=!N%5h&!n1uJYG&0j+R3`oxjg>w`QnCz zlMbeR+BqjdW%BWSVcaWXdsAHvcl2$gvCzJ{Er)Gt7|;rvdcxmUq=Zq#MV_LKDso0| zYiQ_s>m~Z9dli0TGO6A|9#zlky%S)>!?hX5bwNfjll*4y;Zdu!g0R4my&(@-m<^w9 zi#{e6rFloPX{Xi|^NQ>c-hR%#-|BPP&OaIHGH~TIv}3i^E?qqp$$Ac%IVAl2^=M!e z@#~jfPUGRDgp=3Ecot^95i(~=b* zS@4zYsn{3O_uM;wq{NWzP0wJfz~=CK4?RE5G53|!%-y)b+MsTy^{g+uD-E}hqqcsFa}sNe9oK~1X+C0PF| zUAN07IcOA?$}QSM7Q>{M&+(sWl<0p@XQo!9`JN9ma$sM3jY-b-5`(IyxBxd3O#|LT zX&>z}@Bc2N?;L=8PAQrGEn%?qwwEFY_<;A4WsYd zY%0JN+-bO_b7=IA0Wm?mIlGcSOlE@f)!rlz;=n<{eDg@l+*(Yn?D_wp~QAkm!S$eF7iWkDYhC)B^YM*Uoj-%u8K$ z>8RsVrd92MRr$DU(r{=Q^eaY7MhS6CS=QYRai{Ej;g- z+^0eAJSA(%>MA?k6W4sCHmPQ+WM`CxRj!FSS%Cud(B){G>uRL? 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