calcul entam 2nde
authorDenise sur Titasmo <denise.maurice@normalesup.org>
Wed, 1 Jun 2016 17:24:49 +0000 (19:24 +0200)
committerDenise sur Titasmo <denise.maurice@normalesup.org>
Wed, 1 Jun 2016 17:24:49 +0000 (19:24 +0200)
2nde/calcul_mental/arbreproba.pdf [new file with mode: 0644]
2nde/calcul_mental/arbreproba.svg [new file with mode: 0644]
2nde/calcul_mental/arbres_probabilites.pdf [new file with mode: 0644]
2nde/calcul_mental/arbres_probabilites.tex [new file with mode: 0644]

diff --git a/2nde/calcul_mental/arbreproba.pdf b/2nde/calcul_mental/arbreproba.pdf
new file mode 100644 (file)
index 0000000..7b05f66
Binary files /dev/null and b/2nde/calcul_mental/arbreproba.pdf differ
diff --git a/2nde/calcul_mental/arbreproba.svg b/2nde/calcul_mental/arbreproba.svg
new file mode 100644 (file)
index 0000000..ceb19a7
--- /dev/null
@@ -0,0 +1,240 @@
+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!-- Created with Inkscape (http://www.inkscape.org/) -->
+
+<svg
+   xmlns:dc="http://purl.org/dc/elements/1.1/"
+   xmlns:cc="http://creativecommons.org/ns#"
+   xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
+   xmlns:svg="http://www.w3.org/2000/svg"
+   xmlns="http://www.w3.org/2000/svg"
+   xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd"
+   xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape"
+   width="42.898994mm"
+   height="38.850151mm"
+   viewBox="0 0 152.00431 137.65801"
+   id="svg2"
+   version="1.1"
+   inkscape:version="0.91 r"
+   sodipodi:docname="arbreproba.svg">
+  <defs
+     id="defs4" />
+  <sodipodi:namedview
+     id="base"
+     pagecolor="#ffffff"
+     bordercolor="#666666"
+     borderopacity="1.0"
+     inkscape:pageopacity="0.0"
+     inkscape:pageshadow="2"
+     inkscape:zoom="2.8"
+     inkscape:cx="53.248037"
+     inkscape:cy="70.57792"
+     inkscape:document-units="px"
+     inkscape:current-layer="layer1"
+     showgrid="false"
+     inkscape:window-width="1366"
+     inkscape:window-height="716"
+     inkscape:window-x="0"
+     inkscape:window-y="0"
+     inkscape:window-maximized="1"
+     fit-margin-top="0"
+     fit-margin-left="0"
+     fit-margin-right="0"
+     fit-margin-bottom="0" />
+  <metadata
+     id="metadata7">
+    <rdf:RDF>
+      <cc:Work
+         rdf:about="">
+        <dc:format>image/svg+xml</dc:format>
+        <dc:type
+           rdf:resource="http://purl.org/dc/dcmitype/StillImage" />
+        <dc:title></dc:title>
+      </cc:Work>
+    </rdf:RDF>
+  </metadata>
+  <g
+     inkscape:label="Calque 1"
+     inkscape:groupmode="layer"
+     id="layer1"
+     transform="translate(-264.07339,-465.2821)">
+    <path
+       style="fill:none;fill-rule:evenodd;stroke:#000000;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
+       d="m 323.21429,500.21935 -57.5,38.21428 59.64285,0.35715"
+       id="path3336"
+       inkscape:connector-curvature="0" />
+    <path
+       style="fill:none;fill-rule:evenodd;stroke:#000000;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
+       d="m 265.35714,537.3622 c 2.85715,0.35715 56.42857,39.28572 56.42857,39.28572"
+       id="path3338"
+       inkscape:connector-curvature="0" />
+    <path
+       style="fill:none;fill-rule:evenodd;stroke:#000000;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
+       d="M 400,475.93363 347.85714,496.64792 400,505.93363"
+       id="path3340"
+       inkscape:connector-curvature="0" />
+    <path
+       style="fill:none;fill-rule:evenodd;stroke:#000000;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
+       d="m 402.24519,519.13413 -52.14286,20.71429 52.14286,9.28571"
+       id="path3340-0"
+       inkscape:connector-curvature="0" />
+    <path
+       style="fill:none;fill-rule:evenodd;stroke:#000000;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
+       d="m 400.81662,563.41984 -52.14286,20.71429 52.14286,9.28571"
+       id="path3340-8"
+       inkscape:connector-curvature="0" />
+    <text
+       xml:space="preserve"
+       style="font-style:normal;font-weight:normal;font-size:22.5px;line-height:125%;font-family:Sans;letter-spacing:0px;word-spacing:0px;fill:#d10000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1;"
+       x="328.57144"
+       y="504.86221"
+       id="text3363"
+       sodipodi:linespacing="125%"><tspan
+         sodipodi:role="line"
+         id="tspan3365"
+         x="328.57144"
+         y="504.86221">R</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-style:normal;font-weight:normal;font-size:22.5px;line-height:125%;font-family:Sans;letter-spacing:0px;word-spacing:0px;fill:#0000c9;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1;"
+       x="331.76035"
+       y="545.92065"
+       id="text3363-5"
+       sodipodi:linespacing="125%"><tspan
+         sodipodi:role="line"
+         id="tspan3365-6"
+         x="331.76035"
+         y="545.92065">B</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-style:normal;font-weight:normal;font-size:22.5px;line-height:125%;font-family:Sans;letter-spacing:0px;word-spacing:0px;fill:#00d100;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1;"
+       x="328.9032"
+       y="590.20636"
+       id="text3363-5-3"
+       sodipodi:linespacing="125%"><tspan
+         sodipodi:role="line"
+         id="tspan3365-6-3"
+         x="328.9032"
+         y="590.20636">V</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-style:normal;font-weight:normal;font-size:20px;line-height:125%;font-family:Sans;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
+       x="402.5"
+       y="479.86218"
+       id="text3403"
+       sodipodi:linespacing="125%"><tspan
+         sodipodi:role="line"
+         id="tspan3405"
+         x="402.5"
+         y="479.86218">P</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-style:normal;font-weight:normal;font-size:20px;line-height:125%;font-family:Sans;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
+       x="401.90152"
+       y="509.2951"
+       id="text3403-7"
+       sodipodi:linespacing="125%"><tspan
+         sodipodi:role="line"
+         id="tspan3405-5"
+         x="401.90152"
+         y="509.2951">F</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-style:normal;font-weight:normal;font-size:20px;line-height:125%;font-family:Sans;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
+       x="404.70074"
+       y="524.93579"
+       id="text3403-6"
+       sodipodi:linespacing="125%"><tspan
+         sodipodi:role="line"
+         id="tspan3405-0"
+         x="404.70074"
+         y="524.93579">P</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-style:normal;font-weight:normal;font-size:20px;line-height:125%;font-family:Sans;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
+       x="404.10226"
+       y="554.36871"
+       id="text3403-7-8"
+       sodipodi:linespacing="125%"><tspan
+         sodipodi:role="line"
+         id="tspan3405-5-1"
+         x="404.10226"
+         y="554.36871">F</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-style:normal;font-weight:normal;font-size:20px;line-height:125%;font-family:Sans;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
+       x="404.70074"
+       y="573.5072"
+       id="text3403-9"
+       sodipodi:linespacing="125%"><tspan
+         sodipodi:role="line"
+         id="tspan3405-2"
+         x="404.70074"
+         y="573.5072">P</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-style:normal;font-weight:normal;font-size:20px;line-height:125%;font-family:Sans;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
+       x="404.10226"
+       y="602.94012"
+       id="text3403-7-9"
+       sodipodi:linespacing="125%"><tspan
+         sodipodi:role="line"
+         id="tspan3405-5-4"
+         x="404.10226"
+         y="602.94012">F</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-style:normal;font-weight:normal;font-size:15px;line-height:125%;font-family:Sans;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
+       x="275"
+       y="515.57648"
+       id="text3461"
+       sodipodi:linespacing="125%"><tspan
+         sodipodi:role="line"
+         id="tspan3463"
+         x="275"
+         y="515.57648">1/5</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-style:normal;font-weight:normal;font-size:15px;line-height:125%;font-family:Sans;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
+       x="280.96451"
+       y="574.63397"
+       id="text3461-8-5"
+       sodipodi:linespacing="125%"><tspan
+         sodipodi:role="line"
+         id="tspan3463-2-1"
+         x="280.96451"
+         y="574.63397">2/5</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-style:normal;font-weight:normal;font-size:15px;line-height:125%;font-family:Sans;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
+       x="362.75024"
+       y="481.41965"
+       id="text3461-8-3"
+       sodipodi:linespacing="125%"><tspan
+         sodipodi:role="line"
+         id="tspan3463-2-5"
+         x="362.75024"
+         y="481.41965">1/2</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-style:normal;font-weight:normal;font-size:15px;line-height:125%;font-family:Sans;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
+       x="362.84546"
+       y="512.94708"
+       id="text3461-8-3-9"
+       sodipodi:linespacing="125%"><tspan
+         sodipodi:role="line"
+         id="tspan3463-2-5-9"
+         x="362.84546"
+         y="512.94708">1/2</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-style:normal;font-weight:normal;font-size:15px;line-height:125%;font-family:Sans;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
+       x="364.46646"
+       y="600.71729"
+       id="text3461-8-3-9-1"
+       sodipodi:linespacing="125%"><tspan
+         sodipodi:role="line"
+         id="tspan3463-2-5-9-1"
+         x="364.46646"
+         y="600.71729">1/2</tspan></text>
+  </g>
+</svg>
diff --git a/2nde/calcul_mental/arbres_probabilites.pdf b/2nde/calcul_mental/arbres_probabilites.pdf
new file mode 100644 (file)
index 0000000..50750df
Binary files /dev/null and b/2nde/calcul_mental/arbres_probabilites.pdf differ
diff --git a/2nde/calcul_mental/arbres_probabilites.tex b/2nde/calcul_mental/arbres_probabilites.tex
new file mode 100644 (file)
index 0000000..e092dbe
--- /dev/null
@@ -0,0 +1,96 @@
+\input{../../header_beamer.tex}
+%%%%%%%%%%%% partie à modifier
+
+\newcommand\titre{Probabilités}
+
+\newcommand\consigne{On tire une boule dans une urne, contenant 2 boules rouges, 4 boules vertes et 4 boules bleues.
+
+}
+\newcommand\qa{
+Décrire l'univers de cette expérience.}
+\newcommand\ra{$\Omega = \{ R; B; V\}$}
+\newcommand\qb{Donner la loi de probabilité de cette expérience.}
+\newcommand\rb{\begin{tabular}{|c|c|c|c|}
+\hline
+Issue & R & B & V \\
+\hline
+Proba & $\frac{1}{5}$ & $\frac{2}{5}$ & $\frac{2}{5}$ \\
+\hline
+\end{tabular}}
+\newcommand\qc{Après le tirage de l'urne, on tire à pile ou face avec une pièce équilibrée. Décrire l'univers de cette nouvelle expérience.
+
+\includegraphics[width=0.4\textwidth]{arbreproba.pdf}
+}
+\newcommand\rc{$\Omega = \{RP; RF; BP; BF; VP; VF \}$}
+\newcommand\qd{Quelles sont les probabilités manquantes sur les branches de l'arbre ?}
+\newcommand\rd{$\frac{2}{5}$ sur la branche de gauche, $\frac{1}{2}$ sur les autres}
+\newcommand\qe{Calculer la probabilité de l'issue \og VF \fg}
+\newcommand\re{$p(VF) = \frac{2}{5} \times \frac{1}{2}$}
+
+%%%%%%%%%%%%%%%
+
+
+\begin{document}
+\slide{\titre
+
+\bigskip \pause
+
+\consigne}
+
+\slide{\consigne
+
+\begin{enumerate}[1)]
+\item \qa
+\end{enumerate}
+}
+
+\slide{\consigne
+
+\begin{enumerate}[1)]
+\setcounter{enumi}{1}
+\item \qb
+\end{enumerate}
+}
+\slide{\consigne
+
+\begin{enumerate}[1)]
+\setcounter{enumi}{2}
+\item \qc
+\end{enumerate}
+}
+
+\slide{
+\includegraphics[width=0.5\textwidth]{arbreproba.pdf}
+
+\begin{enumerate}[1)]
+\setcounter{enumi}{3}
+\item \qd
+\end{enumerate}
+}
+\slide{
+\includegraphics[width=0.5\textwidth]{arbreproba.pdf}
+
+\begin{enumerate}[1)]
+\setcounter{enumi}{4}
+\item \qe
+\end{enumerate}
+}
+
+\slide{\consigne
+\begin{enumerate}[1)]
+\item \qa~\reponse{2}{\ra}
+\item \qb~\reponse{3}{\rb}
+\end{enumerate}
+}
+
+\slide{
+\begin{enumerate}[1)]
+\setcounter{enumi}{3}
+\item \qc~\reponse{2}{\rc}
+\item \qd~\reponse{3}{\rd}
+\item \qe~\reponse{4}{\re}
+\end{enumerate}
+
+
+}
+\end{document}