QCM corrigé dénombrement et probabilité 1 mathématique, QCM arrangement, QCM dénombrement, QCM permutation, QCM probabilité 18 h 27 <html xml:lang="en" xmlns="http://www.w3.org/1998/Math/MathML"> <head> <title>QCM dénombrement et probabilité corrigé </title> <script src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_SVG" type="text/javascript"></script> </head> <body> <!-- MathMagic Pro Win v8.0, MathML 2.0 converter, 2015.6.14 21:59 --> <math xmlns="http://www.w3.org/1998/Math/MathML"> <semantics> <mstyle> <mtable> <mtr> <mtd columnalign="left"> <mi mathcolor="#0000ff" mathsize="14.2pt">QCM</mi> <mspace width="0.33em"> <mi mathcolor="#0000ff" mathsize="14.2pt">d</mi> <mo mathcolor="#0000ff" mathsize="14.2pt">é</mo> <mi mathcolor="#0000ff" mathsize="14.2pt">n</mi> <mi mathcolor="#0000ff" mathsize="14.2pt">o</mi> <mi mathcolor="#0000ff" mathsize="14.2pt">m</mi> <mi mathcolor="#0000ff" mathsize="14.2pt">b</mi> <mi mathcolor="#0000ff" mathsize="14.2pt">r</mi> <mi 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mathcolor="#0000ff">e</mi> <mi mathcolor="#0000ff">s</mi> <mi mathcolor="#0000ff">t</mi> <mi mathcolor="#0000ff">i</mi> <mi mathcolor="#0000ff">o</mi> <mi mathcolor="#0000ff">n</mi> <mn mathcolor="#0000ff">1</mn> </mtd> </mtr> <mtr> <mtd columnalign="left"> <mi>Soit</mi> <mspace width="0.33em"> <mi>S</mi> <mspace width="0.33em"> <mi>l</mi> <mi>'</mi> <mi>e</mi> <mi>n</mi> <mi>s</mi> <mi>e</mi> <mi>m</mi> <mi>b</mi> <mi>l</mi> <mi>e</mi> <mspace width="0.33em"> <mi>fini</mi> <mspace width="0.33em"> <mi>de</mi> <mspace width="0.33em"> <mi>cardinal</mi> <mspace width="0.33em"> <mi>n</mi> <mspace width="0.33em"> <mi>et</mi> <mspace width="0.33em"> <mo>P</mo> <mfenced close=")" open="("> <mi>S</mi> </mfenced> <mspace width="0.33em"> <mi>l</mi> <mi>'</mi> <mi>e</mi> <mi>n</mi> <mi>s</mi> <mi>e</mi> <mi>m</mi> <mi>b</mi> <mi>l</mi> <mi>e</mi> <mspace width="0.33em"> <mi>des</mi> <mspace width="0.33em"> <mi>parties</mi> <mspace width="0.33em"> <mi>A</mi> <mspace width="0.33em"> <mi>de</mi> <mspace width="0.33em"> <mi>S</mi> <mspace width="0.33em"> <mi>,</mi> <mi>a</mi> <mi>l</mi> <mi>o</mi> <mi>r</mi> <mi>s</mi> <mspace width="0.33em"> <mrow> <munder> <mo>∑</mo> <mrow> <mi>A</mi> <mo mathsize="14.2pt">∊</mo> <mo>P</mo> <mfenced close=")" open="("> <mi>S</mi> </mfenced> </mrow> </munder> <mi mathsize="8.5pt">CardA</mi> </mrow> </mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mtd> </mtr> <mtr> <mtd columnalign="left"> <mi>est</mi> <mspace width="0.33em"> <mo>é</mo> <mi>gale</mi> <mi>:</mi> </mspace></mtd> </mtr> <mtr> <mtd columnalign="left"> <mo>□</mo> <mspace width="0.33em"> <msup> <mn>2</mn> <mi mathsize="8.5pt">n</mi> </msup> </mspace></mtd> </mtr> <mtr> <mtd columnalign="left"> <mo>□</mo> <mspace width="0.33em"> <msup> <mrow> <mi>n</mi> <mn>2</mn> </mrow> <mi mathsize="8.5pt">n</mi> </msup> </mspace></mtd> </mtr> <mtr> <mtd columnalign="left"> <mo>☑</mo> <mspace width="0.33em"> <msup> <mrow> <mi>n</mi> <mn>2</mn> </mrow> <mrow> <mi mathsize="8.5pt">n</mi> <mo mathsize="8.5pt">−</mo> <mn mathsize="8.5pt">1</mn> </mrow> </msup> </mspace></mtd> </mtr> <mtr> <mtd columnalign="left"> <mo>□</mo> <mspace width="0.33em"> <msup> <mi>n</mi> <mi mathsize="8.5pt">n</mi> </msup> </mspace></mtd> </mtr> <mtr> <mtd columnalign="left"> <mi mathcolor="#0000ff">Q</mi> <mi mathcolor="#0000ff">u</mi> <mi mathcolor="#0000ff">e</mi> <mi mathcolor="#0000ff">s</mi> <mi mathcolor="#0000ff">t</mi> <mi mathcolor="#0000ff">i</mi> <mi mathcolor="#0000ff">o</mi> <mi mathcolor="#0000ff">n</mi> <mn mathcolor="#0000ff">2</mn> </mtd> </mtr> <mtr> <mtd columnalign="left"> <mi>On</mi> <mspace width="0.33em"> <mi>propose</mi> <mspace width="0.33em"> <mo>à</mo> <mspace width="0.33em"> <mi>un</mi> <mspace width="0.33em"> <mi>candidat</mi> <mspace width="0.33em"> <mi>un</mi> <mspace width="0.33em"> <mi>QCM</mi> <mspace width="0.33em"> <mi>de</mi> <mspace width="0.33em"> <mn>60</mn> <mspace width="0.33em"> <mi>q</mi> <mi>u</mi> <mi>e</mi> <mi>s</mi> <mi>t</mi> <mi>i</mi> <mi>o</mi> <mi>n</mi> <mi>s</mi> <mi>.</mi> <mi>p</mi> <mi>o</mi> <mi>u</mi> <mi>r</mi> <mspace width="0.33em"> <mi>chaque</mi> <mspace width="0.33em"> <mi>question</mi> <mspace width="0.33em"> <mi>il</mi> <mspace width="0.33em"> <mi>y</mi> <mspace width="0.33em"> <mi>a</mi> <mspace width="0.33em"> <mn>4</mn> <mspace width="0.33em"> <mi>réponses</mi> <mspace width="0.33em"> </mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mtd> </mtr> <mtr> <mtd columnalign="left"> <mi>possibles</mi> <mspace width="0.33em"> <mi>dont</mi> <mspace width="0.33em"> <mi>une</mi> <mspace width="0.33em"> <mi>seule</mi> <mspace width="0.33em"> <mi>est</mi> <mspace width="0.33em"> <mi>c</mi> <mi>o</mi> <mi>r</mi> <mi>r</mi> <mi>é</mi> <mi>c</mi> <mi>t</mi> <mi>e</mi> <mi>.</mi> </mspace></mspace></mspace></mspace></mspace></mtd> </mtr> <mtr> <mtd columnalign="left"> <mi>Ce</mi> <mspace width="0.33em"> <mi>candidat</mi> <mspace width="0.33em"> <mi>doit</mi> <mspace width="0.33em"> <mi>répondre</mi> <mspace width="0.33em"> <mi>au</mi> <mspace width="0.33em"> <mi>hasard</mi> <mspace width="0.33em"> <mo>à</mo> <mspace width="0.33em"> <mi>ce</mi> <mspace width="0.33em"> <mi>questionnaire</mi> <mspace width="0.33em"> <mi>,</mi> <mi>la</mi> <mspace width="0.33em"> <mi>probabilité</mi> <mspace width="0.33em"> <mi>que</mi> <mspace width="0.33em"> <mi>toutes</mi> <mspace width="0.33em"> <mi>ces</mi> <mspace width="0.33em"> <mi>réponses</mi> <mspace width="0.33em"> </mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mtd> </mtr> <mtr> <mtd columnalign="left"> <mi>soient</mi> <mspace width="0.33em"> <mi>justes</mi> <mspace width="0.33em"> <mi>est</mi> <mspace width="0.33em"> <mi>:</mi> </mspace></mspace></mspace></mtd> </mtr> <mtr> <mtd columnalign="left"> <mo>□</mo> <mspace width="0.33em"> <mstyle mathsize="15.6pt"> <mfrac> <mn>1</mn> <mn>4</mn> </mfrac> </mstyle> </mspace></mtd> </mtr> <mtr> <mtd columnalign="left"> <mo>□</mo> <mspace width="0.33em"> <mstyle mathsize="12.8pt"> <mfrac> <mrow> <mstyle mathsize="12.0pt"> <mfenced close=")" open="("> <mrow> <mn mathsize="12.8pt">60</mn> <mo mathsize="12.8pt">−</mo> <mn mathsize="12.8pt">4</mn> </mrow> </mfenced> </mstyle> <mi>!</mi> </mrow> <mrow> <mn>6</mn> <mn>0</mn> <mi>!</mi> </mrow> </mfrac> </mstyle> </mspace></mtd> </mtr> <mtr> <mtd columnalign="left"> <mo>□</mo> <mspace width="0.33em"> <mstyle mathsize="14.2pt"> <mfrac> <mn>1</mn> <msup> <mn>60</mn> <mn>4</mn> </msup> </mfrac> </mstyle> </mspace></mtd> </mtr> <mtr> <mtd columnalign="left"> <mo mathsize="12.8pt">☑</mo> <mspace width="0.33em"> <mstyle mathsize="15.7pt"> <mfrac> <mn>1</mn> <msup> <mn>4</mn> <mn>60</mn> </msup> </mfrac> </mstyle> </mspace></mtd> </mtr> <mtr> <mtd columnalign="left"> <mi mathcolor="#0000ff">Q</mi> <mi mathcolor="#0000ff">u</mi> <mi mathcolor="#0000ff">e</mi> <mi mathcolor="#0000ff">s</mi> <mi mathcolor="#0000ff">t</mi> <mi mathcolor="#0000ff">i</mi> <mi mathcolor="#0000ff">o</mi> <mi mathcolor="#0000ff">n</mi> <mn mathcolor="#0000ff">3</mn> </mtd> </mtr> <mtr> <mtd columnalign="left"> <mi>Une</mi> <mspace width="0.33em"> <mi>urne</mi> <mspace width="0.33em"> <mi>contient</mi> <mspace width="0.33em"> <mn>7</mn> <mspace width="0.33em"> <mi>boules</mi> <mspace width="0.33em"> <mi>rouges</mi> <mspace width="0.33em"> <mi>et</mi> <mspace width="0.33em"> <mn>3</mn> <mspace width="0.33em"> <mi>boule</mi> <mspace width="0.33em"> <mi>noires</mi> <mspace width="0.33em"> <mi>indiscernables</mi> <mspace width="0.33em"> <mi>au</mi> <mspace width="0.33em"> <mi>t</mi> <mi>o</mi> <mi>u</mi> <mi>c</mi> <mi>h</mi> <mi>e</mi> <mi>r</mi> <mi>.</mi> <mspace width="0.33em"> <mi>on</mi> </mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mtd> </mtr> <mtr> <mtd columnalign="left"> <mi>tire</mi> <mspace width="0.33em"> <mi>succesivement</mi> <mspace width="0.33em"> <mi>et</mi> <mspace width="0.33em"> <mi>avec</mi> <mspace width="0.33em"> <mi>remise</mi> <mspace width="0.33em"> <mi>n</mi> <mspace width="0.33em"> <mi>boules</mi> <mspace width="0.33em"> <mi>n</mi> <mi>o</mi> <mi>i</mi> <mi>r</mi> <mi>e</mi> <mi>s</mi> <mi>,</mi> <mspace width="0.33em"> <mi>ou</mi> <mspace width="0.33em"> <mi>n</mi> <mo>∊</mo> <msup> <mi>N</mi> <mo>*</mo> </msup> <mspace width="0.33em"> <mi>.</mi> <mi>L</mi> <mi>a</mi> <mspace width="0.33em"> <mi>probabilité</mi> <mspace width="0.33em"> <mi>d</mi> <mi>'</mi> <mi>o</mi> <mi>b</mi> <mi>t</mi> <mi>e</mi> <mi>n</mi> <mi>i</mi> <mi>r</mi> </mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mtd> </mtr> <mtr> <mtd columnalign="left"> <mi>au</mi> <mspace width="0.33em"> <mi>moins</mi> <mspace width="0.33em"> <mi>une</mi> <mspace width="0.33em"> <mi>boule</mi> <mspace width="0.33em"> <mi>noire</mi> <mspace width="0.33em"> <mi>est</mi> <mspace width="0.33em"> <mo>é</mo> <mi>g</mi> <mi>a</mi> <mi>l</mi> <mi>e</mi> <mi>:</mi> </mspace></mspace></mspace></mspace></mspace></mspace></mtd> </mtr> <mtr> <mtd columnalign="left"> <mo>□</mo> <mspace width="0.33em"> <msup> <mstyle mathsize="12.0pt"> <mfenced close=")" open="("> <mstyle mathsize="14.2pt"> <mfrac> <mn>3</mn> <mn>10</mn> </mfrac> </mstyle> </mfenced> </mstyle> <mi mathsize="8.5pt">n</mi> </msup> </mspace></mtd> </mtr> <mtr> <mtd columnalign="left"> <mo>□</mo> <mspace width="0.33em"> <msup> <mstyle mathsize="12.0pt"> <mfenced close=")" open="("> <mstyle mathsize="14.2pt"> <mfrac> <mn>7</mn> <mn>10</mn> </mfrac> </mstyle> </mfenced> </mstyle> <mi mathsize="8.5pt">n</mi> </msup> </mspace></mtd> </mtr> <mtr> <mtd columnalign="left"> <mo>□</mo> <mspace width="0.33em"> <mn>1</mn> <mo>−</mo> <msup> <mstyle mathsize="12.0pt"> <mfenced close=")" open="("> <mstyle mathsize="14.2pt"> <mfrac> <mn>3</mn> <mn>10</mn> </mfrac> </mstyle> </mfenced> </mstyle> <mi mathsize="8.5pt">n</mi> </msup> </mspace></mtd> </mtr> <mtr> <mtd columnalign="left"> <mo>☑</mo> <mspace width="0.33em"> <mn>1</mn> <mo>−</mo> <msup> <mstyle mathsize="12.0pt"> <mfenced close=")" open="("> <mstyle mathsize="14.2pt"> <mfrac> <mn>7</mn> <mn>10</mn> </mfrac> </mstyle> </mfenced> </mstyle> <mi mathsize="8.5pt">n</mi> </msup> </mspace></mtd> </mtr> <mtr> <mtd columnalign="left"> <mi mathcolor="#0000ff">Q</mi> <mi mathcolor="#0000ff">u</mi> <mi mathcolor="#0000ff">e</mi> <mi mathcolor="#0000ff">s</mi> <mi mathcolor="#0000ff">t</mi> <mi mathcolor="#0000ff">i</mi> <mi mathcolor="#0000ff">o</mi> <mi mathcolor="#0000ff">n</mi> <mn mathcolor="#0000ff">4</mn> </mtd> </mtr> <mtr> <mtd columnalign="left"> <mi>Soit</mi> <mspace width="0.33em"> <mi>E</mi> <mspace width="0.33em"> <mi>l</mi> <mi>'</mi> <mi>e</mi> <mi>n</mi> <mi>s</mi> <mi>e</mi> <mi>m</mi> <mi>b</mi> <mi>l</mi> <mi>e</mi> <mspace width="0.33em"> <mi>de</mi> <mspace width="0.33em"> <mn>5</mn> <mspace width="0.33em"> <mi>chiffres</mi> <mspace width="0.33em"> <mi>qui</mi> <mspace width="0.33em"> <mi>contiennent</mi> <mspace width="0.33em"> <mn>0</mn> <mspace width="0.33em"> <mi>une</mi> <mspace width="0.33em"> <mi>seule</mi> <mspace width="0.33em"> <mi>f</mi> <mi>o</mi> <mi>i</mi> <mi>s</mi> <mi>.</mi> <mspace width="0.33em"> <mi>Card</mi> <mfenced close=")" open="("> <mi>E</mi> </mfenced> <mspace width="0.33em"> <mi>est</mi> <mspace width="0.33em"> <mo>é</mo> <mi>gal</mi> <mspace width="0.33em"> <mi>:</mi> </mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mtd> </mtr> <mtr> <mtd columnalign="left"> <mo>□</mo> <mspace width="0.33em"> <mn>9</mn> <mi>!</mi> </mspace></mtd> </mtr> <mtr> <mtd columnalign="left"> <mo>□</mo> <mspace width="0.33em"> <msup> <mn>9</mn> <mn>5</mn> </msup> </mspace></mtd> </mtr> <mtr> <mtd columnalign="left"> <mo>☑</mo> <mspace width="0.33em"> <mn>4</mn> <mo>×</mo> <msup> <mn>9</mn> <mn>4</mn> </msup> </mspace></mtd> </mtr> <mtr> <mtd columnalign="left"> <mo>□</mo> <mspace width="0.33em"> <msup> <mn>5</mn> <mn>9</mn> </msup> </mspace></mtd> </mtr> <mtr> <mtd columnalign="left"> <mi mathcolor="#0000ff">Q</mi> <mi mathcolor="#0000ff">u</mi> <mi mathcolor="#0000ff">e</mi> <mi mathcolor="#0000ff">s</mi> <mi mathcolor="#0000ff">t</mi> <mi mathcolor="#0000ff">i</mi> <mi mathcolor="#0000ff">o</mi> <mi mathcolor="#0000ff">n</mi> <mn mathcolor="#0000ff">5</mn> </mtd> </mtr> <mtr> <mtd columnalign="left"> <mn>360</mn> <mspace width="0.33em"> <mi>personnes</mi> <mspace width="0.33em"> <mi>ont</mi> <mspace width="0.33em"> <mi>leurs</mi> <mspace width="0.33em"> <mi>anniversaires</mi> <mspace width="0.33em"> <mo>à</mo> <mspace width="0.33em"> <mi>des</mi> <mspace width="0.33em"> <mi>dates</mi> <mspace width="0.33em"> <mi>toutes</mi> <mspace width="0.33em"> <mi>distinctes</mi> <mspace width="0.33em"> <mi>dans</mi> <mspace width="0.33em"> <mi>l</mi> <mi>'</mi> <mi>a</mi> <mi>n</mi> <mi>n</mi> <mi>é</mi> <mi>e</mi> <mspace width="0.33em"> <mi>de</mi> <mspace width="0.33em"> <mn>365</mn> <mspace width="0.33em"> <mi>j</mi> <mi>o</mi> <mi>u</mi> <mi>r</mi> <mi>s</mi> <mi>.</mi> </mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mtd> </mtr> <mtr> <mtd columnalign="left"> <mi>Combien</mi> <mspace width="0.33em"> <mi>y</mi> <mo>−</mo> <mi>a</mi> <mo>−</mo> <mi>t</mi> <mo>−</mo> <mi>il</mi> <mspace width="0.33em"> <mi>de</mi> <mspace width="0.33em"> <mi>calendriers</mi> <mspace width="0.33em"> <mi>d</mi> <mi>'</mi> <mi>a</mi> <mi>n</mi> <mi>n</mi> <mi>i</mi> <mi>v</mi> <mi>e</mi> <mi>r</mi> <mi>s</mi> <mi>a</mi> <mi>i</mi> <mi>r</mi> <mi>e</mi> <mi>s</mi> <mspace width="0.33em"> <mi>possibles</mi> <mspace width="0.33em"> <mi>?</mi> </mspace></mspace></mspace></mspace></mspace></mspace></mtd> </mtr> <mtr> <mtd columnalign="left"> <mo>□</mo> <mspace width="0.33em"> <mn>360</mn> <mi>!</mi> <msubsup> <mi>C</mi> <mn>365</mn> <mn>5</mn> </msubsup> </mspace></mtd> </mtr> <mtr> <mtd columnalign="left"> <mo>□</mo> <mspace width="0.33em"> <mn>360</mn> <mi>!</mi> <msubsup> <mi>A</mi> <mn>365</mn> <mn>5</mn> </msubsup> </mspace></mtd> </mtr> <mtr> <mtd columnalign="left"> <mo>☑</mo> <mspace width="0.33em"> <msubsup> <mi>C</mi> <mn>365</mn> <mn>360</mn> </msubsup> </mspace></mtd> </mtr> <mtr> <mtd columnalign="left"> <mo>□</mo> <mspace width="0.33em"> <msubsup> <mi>A</mi> <mn>365</mn> <mn>360</mn> </msubsup> </mspace></mtd> </mtr> <mtr> <mtd columnalign="left"> <mi mathcolor="#0000ff">Question</mi> <mn mathcolor="#0000ff">6</mn> </mtd> </mtr> <mtr> <mtd columnalign="left"> <mi>Une</mi> <mspace width="0.33em"> <mi>urne</mi> <mspace width="0.33em"> <mi>contient</mi> <mspace width="0.33em"> <mi>x</mi> <mspace width="0.33em"> <mi>boules</mi> <mspace width="0.33em"> <mi>dont</mi> <mspace width="0.33em"> <mn>3</mn> <mspace width="0.33em"> <mi>sont</mi> <mspace width="0.33em"> <mi>blanches</mi> <mi>,</mi> <mi>les</mi> <mspace width="0.33em"> <mi>autres</mi> <mspace width="0.33em"> <mo>é</mo> <mi>tan</mi> <mi>t</mi> <mspace width="0.33em"> <mi>rouges</mi> <mi>.</mi> </mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mtd> </mtr> <mtr> <mtd columnalign="left"> <mi>A</mi> <mspace width="0.33em"> <mi>l</mi> <mo>’</mo> <mi>occasion</mi> <mspace width="0.33em"> <mi>du</mi> <mspace width="0.33em"> <mi>tirage</mi> <mi>,</mi> <mi>sans</mi> <mspace width="0.33em"> <mi>remise</mi> <mi>,</mi> <mi>de</mi> <mspace width="0.33em"> <mi>deux</mi> <mspace width="0.33em"> <mi>boules</mi> <mi>,</mi> <mspace width="0.33em"> <mi>la</mi> <mspace width="0.33em"> <mi>probabilit</mi> <mo>é</mo> <mspace width="0.33em"> <mi>d</mi> <mo>’</mo> <mi>obtenir</mi> <mspace width="0.33em"> <mi>une</mi> <mspace width="0.33em"> <mi>boule</mi> <mspace width="0.33em"> <mi>blanche</mi> </mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mtd> </mtr> <mtr> <mtd columnalign="left"> <mi>puis</mi> <mspace width="0.33em"> <mi>une</mi> <mspace width="0.33em"> <mi>boule</mi> <mspace width="0.33em"> <mi>rouge</mi> <mspace width="0.33em"> <mi>est</mi> <mspace width="0.33em"> <mo>é</mo> <mi>gale</mi> <mspace width="0.33em"> <mo>à</mo> <mspace width="0.33em"> <mn>1/4</mn> <mi>.</mi> </mspace></mspace></mspace></mspace></mspace></mspace></mspace></mtd> </mtr> <mtr> <mtd columnalign="left"> <mi>Que</mi> <mspace width="0.33em"> <mi>vaut</mi> <mspace width="0.33em"> <mi>x</mi> <mspace width="0.33em"> <mi>alors</mi> <mi>?</mi> </mspace></mspace></mspace></mtd> </mtr> <mtr> <mtd columnalign="left"> <mo>□</mo> <mspace width="0.33em"> <mi>x</mi> <mo>=</mo> <mn>8</mn> </mspace></mtd> </mtr> <mtr> <mtd columnalign="left"> <mo>□</mo> <mspace width="0.33em"> <mi>x</mi> <mo>=</mo> <mn>12</mn> </mspace></mtd> </mtr> <mtr> <mtd columnalign="left"> <mo>☑</mo> <mspace width="0.33em"> <mi>x</mi> <mo>=</mo> <mn>4</mn> <mspace width="0.33em"> <mi>et</mi> <mspace width="0.33em"> <mi>x</mi> <mo>=</mo> <mn>9</mn> </mspace></mspace></mspace></mtd> </mtr> <mtr> <mtd columnalign="left"> <mo>□</mo> <mspace width="0.33em"> <mi>x</mi> <mo>=</mo> <mn>12</mn> <mspace width="0.33em"> <mi>et</mi> <mspace width="0.33em"> <mi>x</mi> <mo>=</mo> <mn>8</mn> </mspace></mspace></mspace></mtd> </mtr> <mtr> <mtd columnalign="left"> <mi mathcolor="#0000ff">Question</mi> <mn mathcolor="#0000ff">7</mn> </mtd> </mtr> <mtr> <mtd columnalign="left"> <mi>Soit</mi> <mspace width="0.33em"> <mi>b</mi> <mspace width="0.33em"> <mi>et</mi> <mspace width="0.33em"> <mi>n</mi> <mspace width="0.33em"> <mi>deux</mi> <mspace width="0.33em"> <mi>entiers</mi> <mspace width="0.33em"> <mi>naturels</mi> <mspace width="0.33em"> <mi>tels</mi> <mspace width="0.33em"> <mi>que</mi> <mspace width="0.33em"> <mspace width="0.33em"> <mi>b</mi> <mo>></mo> <mn>2</mn> <mspace width="0.33em"> <mi>et</mi> <mspace width="0.33em"> <mi>n</mi> <mo>≥</mo> <mn>2</mn> <mi>.</mi> </mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mtd> </mtr> <mtr> <mtd columnalign="left"> <mi>Une</mi> <mspace width="0.33em"> <mi>urne</mi> <mspace width="0.33em"> <mi>contient</mi> <mspace width="0.33em"> <mn>2</mn> <mspace width="0.33em"> <mi>boules</mi> <mspace width="0.33em"> <mi>blanches</mi> <mspace width="0.33em"> <mi>e</mi> <mi>t</mi> <mi>(</mi> <mi>b</mi> <mo>−</mo> <mn>2</mn> <mi>)</mi> <mspace width="0.33em"> <mi>boules</mi> <mspace width="0.33em"> <mi>n</mi> <mi>o</mi> <mi>i</mi> <mi>r</mi> <mi>e</mi> <mi>s</mi> <mi>,</mi> <mspace width="0.33em"> <mi>indiscernables</mi> <mspace width="0.33em"> <mi>au</mi> <mspace width="0.33em"> <mi>t</mi> <mi>o</mi> <mi>u</mi> <mi>c</mi> <mi>h</mi> <mi>e</mi> <mi>r</mi> <mi>.</mi> </mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mtd> </mtr> <mtr> <mtd columnalign="left"> <mi>On</mi> <mspace width="0.33em"> <mi>tire</mi> <mspace width="0.33em"> <mi>au</mi> <mspace width="0.33em"> <mi>hasar</mi> <mspace width="0.33em"> <mi>d</mi> <mi>'</mi> <mi>u</mi> <mi>n</mi> <mi>e</mi> <mspace width="0.33em"> <mi>boule</mi> <mspace width="0.33em"> <mi>de</mi> <mspace width="0.33em"> <mi>l</mi> <mi>’</mi> <mi>u</mi> <mi>r</mi> <mi>n</mi> <mi>e</mi> <mi>,</mi> <mspace width="0.33em"> <mi>on</mi> <mspace width="0.33em"> <mi>repère</mi> <mspace width="0.33em"> <mi>sa</mi> <mspace width="0.33em"> <mi>couleur</mi> <mspace width="0.33em"> <mi>et</mi> <mspace width="0.33em"> <mi>on</mi> <mspace width="0.33em"> <mi>la</mi> <mspace width="0.33em"> <mi>remet</mi> <mspace width="0.33em"> <mi>dans</mi> <mspace width="0.33em"> <mi>l</mi> <mi>’</mi> <mi>u</mi> <mi>r</mi> <mi>n</mi> <mi>e</mi> <mi>.</mi> </mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mtd> </mtr> <mtr> <mtd columnalign="left"> <mi>On</mi> <mspace width="0.33em"> <mi>répète</mi> <mspace width="0.33em"> <mi>ainsi</mi> <mspace width="0.33em"> <mi>n</mi> <mspace width="0.33em"> <mi>fois</mi> <mspace width="0.33em"> <mi>cette</mi> <mspace width="0.33em"> <mi>e</mi> <mi>x</mi> <mi>p</mi> <mi>é</mi> <mi>r</mi> <mi>i</mi> <mi>e</mi> <mi>n</mi> <mi>c</mi> <mi>e</mi> <mi>.</mi> <mspace width="0.33em"> <mi>On</mi> <mspace width="0.33em"> <mi>désigne</mi> <mspace width="0.33em"> <mi>par</mi> <mspace width="0.33em"> <msub> <mi>p</mi> <mi>n</mi> </msub> <mspace width="0.33em"> <mi>la</mi> <mspace width="0.33em"> <mi>probabilité</mi> <mspace width="0.33em"> <mi>de</mi> <mspace width="0.33em"> <mi>tirer</mi> <mspace width="0.33em"> <mi>une</mi> <mspace width="0.33em"> <mi>boule</mi> <mspace width="0.33em"> <mi>blanche</mi> <mspace width="0.33em"> </mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mtd> </mtr> <mtr> <mtd columnalign="left"> <mi>et</mi> <mspace width="0.33em"> <mi>une</mi> <mspace width="0.33em"> <mi>seule</mi> <mspace width="0.33em"> <mi>lors</mi> <mspace width="0.33em"> <mi>des</mi> <mspace width="0.33em"> <mi>(</mi> <mi>n</mi> <mo>−</mo> <mn>1</mn> <mi>)</mi> <mspace width="0.33em"> <mi>premiers</mi> <mspace width="0.33em"> <mi>tirages</mi> <mspace width="0.33em"> <mi>et</mi> <mspace width="0.33em"> <mi>une</mi> <mspace width="0.33em"> <mi>boule</mi> <mspace width="0.33em"> <mi>noire</mi> <mspace width="0.33em"> <mi>au</mi> <mspace width="0.33em"> <mi>n</mi> <mo>−</mo> <mi>ième</mi> <mspace width="0.33em"> <mi>t</mi> <mi>i</mi> <mi>r</mi> <mi>a</mi> <mi>g</mi> <mi>e</mi> <mi>.</mi> </mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mtd> </mtr> <mtr> <mtd columnalign="left"> <mo>□</mo> <mspace width="0.33em"> <msub> <mi>p</mi> <mn>2</mn> </msub> <mo>=</mo> <mn>1</mn> <mo>−</mo> <mstyle mathsize="14.2pt"> <mfrac> <mn>2</mn> <msup> <mi>b</mi> <mn mathsize="8.5pt">2</mn> </msup> </mfrac> </mstyle> <mspace width="0.33em"> </mspace></mspace></mtd> </mtr> <mtr> <mtd columnalign="left"> <mo>□</mo> <mspace width="0.33em"> <munder> <mi>lim</mi> <mrow> <mi>n</mi> <mo mathsize="50.0%">→</mo> <mo mathsize="50.0%">+</mo> <mo mathsize="50.0%">∞</mo> </mrow> </munder> <mspace width="0.33em"> <msub> <mi>p</mi> <mi>n</mi> </msub> <mo>=</mo> <mo>+</mo> <mo>∞</mo> </mspace></mspace></mtd> </mtr> <mtr> <mtd columnalign="left"> <mo>□</mo> <mspace width="0.33em"> <munder> <mi>lim</mi> <mrow> <mi>n</mi> <mo mathsize="50.0%">→</mo> <mo mathsize="50.0%">+</mo> <mo mathsize="50.0%">∞</mo> </mrow> </munder> <mspace width="0.33em"> <mstyle mathsize="14.2pt"> <mfrac> <msub> <mi>p</mi> <mi>n</mi> </msub> <mrow> <mi>n</mi> <mo>−</mo> <mn>1</mn> </mrow> </mfrac> </mstyle> <mo>=</mo> <mn>1</mn> </mspace></mspace></mtd> </mtr> <mtr> <mtd columnalign="left"> <mo>☑</mo> <mspace width="0.33em"> <msub> <mi>p</mi> <mi>n</mi> </msub> <mo>=</mo> <mstyle mathsize="14.2pt"> <mfrac> <mrow> <mn>2</mn> <mstyle mathsize="12.0pt"> <mfenced close=")" open="("> <mrow> <mi mathsize="14.2pt">n</mi> <mo mathsize="14.2pt">−</mo> <mn mathsize="14.2pt">1</mn> </mrow> </mfenced> </mstyle> </mrow> <mi>b</mi> </mfrac> </mstyle> <mo mathsize="14.2pt">×</mo> <msup> <mstyle mathsize="12.0pt"> <mfenced close=")" open="("> <mrow> <mn mathsize="11.3pt">1</mn> <mo mathsize="14.2pt">−</mo> <mstyle mathsize="14.2pt"> <mfrac> <mn>2</mn> <mi>b</mi> </mfrac> </mstyle> </mrow> </mfenced> </mstyle> <mrow> <mi mathsize="8.5pt">n</mi> <mo mathsize="8.5pt">−</mo> <mn mathsize="8.5pt">1</mn> </mrow> </msup> </mspace></mtd> </mtr> <mtr> <mtd columnalign="left"> <mi mathcolor="#0000ff">Q</mi> <mi mathcolor="#0000ff">u</mi> <mi mathcolor="#0000ff">e</mi> <mi mathcolor="#0000ff">s</mi> <mi mathcolor="#0000ff">t</mi> <mi mathcolor="#0000ff">i</mi> <mi mathcolor="#0000ff">o</mi> <mi mathcolor="#0000ff">n</mi> <mn mathcolor="#0000ff">8</mn> </mtd> </mtr> <mtr> <mtd columnalign="left"> <mi>On</mi> <mspace width="0.33em"> <mi>tire</mi> <mspace width="0.33em"> <mi>au</mi> <mspace width="0.33em"> <mi>hasard</mi> <mspace width="0.33em"> <mi>une</mi> <mspace width="0.33em"> <mi>boule</mi> <mspace width="0.33em"> <mi>dans</mi> <mspace width="0.33em"> <mi>une</mi> <mspace width="0.33em"> <mi>urne</mi> <mspace width="0.33em"> <mi>contenant</mi> <mspace width="0.33em"> <mn>15</mn> <mspace width="0.33em"> <mi>boules</mi> <mspace width="0.33em"> <mi>numérotées</mi> <mspace width="0.33em"> <mi>d</mi> <mi>e</mi> <mn>1</mn> <mspace width="0.33em"> <mo>à</mo> <mspace width="0.33em"> <mn>1</mn> <mn>5</mn> <mi>.</mi> </mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mtd> </mtr> <mtr> <mtd columnalign="left"> <mi>On</mi> <mspace width="0.33em"> <mi>note</mi> <mspace width="0.33em"> <mi>X</mi> <mspace width="0.33em"> <mi>la</mi> <mspace width="0.33em"> <mi>variable</mi> <mspace width="0.33em"> <mi>aléatoire</mi> <mspace width="0.33em"> <mi>prenant</mi> <mspace width="0.33em"> <mi>pour</mi> <mspace width="0.33em"> <mi>valeur</mi> <mspace width="0.33em"> <mi>le</mi> <mspace width="0.33em"> <mi>numéro</mi> <mspace width="0.33em"> <mi>de</mi> <mspace width="0.33em"> <mi>la</mi> <mspace width="0.33em"> <mi>boule</mi> <mspace width="0.33em"> <mi>t</mi> <mi>i</mi> <mi>r</mi> <mi>é</mi> <mi>e</mi> <mi>.</mi> </mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mtd> </mtr> <mtr> <mtd columnalign="left"> <mi>l</mi> <mi>’</mi> <mi>e</mi> <mi>s</mi> <mi>p</mi> <mi>é</mi> <mi>r</mi> <mi>a</mi> <mi>n</mi> <mi>c</mi> <mi>e</mi> <mspace width="0.33em"> <mi>mathématique</mi> <mspace width="0.33em"> <mi>E</mi> <mi>(</mi> <mi>X</mi> <mi>)</mi> <mspace width="0.33em"> <mi>de</mi> <mspace width="0.33em"> <mi>la</mi> <mspace width="0.33em"> <mi>variable</mi> <mspace width="0.33em"> <mi>aléatoire</mi> <mspace width="0.33em"> <mi>X</mi> <mspace width="0.33em"> <mi>vaut</mi> <mspace width="0.33em"> <mi>:</mi> </mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mspace></mtd> </mtr> <mtr> <mtd columnalign="left"> <mo>☑</mo> <mspace width="0.33em"> <mi>E</mi> <mi>(</mi> <mi>X</mi> <mi>)</mi> <mo>=</mo> <mn>8</mn> </mspace></mtd> </mtr> <mtr> <mtd columnalign="left"> <mo>□</mo> <mspace width="0.33em"> <mi>E</mi> <mi>(</mi> <mi>X</mi> <mi>)</mi> <mo>=</mo> <mn>7</mn> </mspace></mtd> </mtr> <mtr> <mtd columnalign="left"> <mo>□</mo> <mspace width="0.33em"> <mi>E</mi> <mi>(</mi> <mi>X</mi> <mi>)</mi> <mo>=</mo> <mstyle 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</semantics> </math> <a href="https://docs.google.com/viewer?a=v&pid=sites&srcid=ZGVmYXVsdGRvbWFpbnxtYXRocWNtfGd4OjZiNGNkMTJlMjg5MjExYmM"><b>TELECHARGER LE QCM EN PDF</b></a> </body> </html> <div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjiMi1nVKaagYEBaG858_cBYvS84wGuxmshNH7c4Li50g9GJu4uv2uhYbegJCgCYFfl9-bt0LXizWaoYvWOdcEhEMm_p1one7gDobbun-NUB1oVyoKpeMF_0ZAFG2V01q925xpPakp7Uo8E/s1600/q2.PNG" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjiMi1nVKaagYEBaG858_cBYvS84wGuxmshNH7c4Li50g9GJu4uv2uhYbegJCgCYFfl9-bt0LXizWaoYvWOdcEhEMm_p1one7gDobbun-NUB1oVyoKpeMF_0ZAFG2V01q925xpPakp7Uo8E/s200/q2.PNG" /></a></div> QCM corrigé dénombrement et probabilité QCM dénombrement et probabilité corrigé QCM ... 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QCM Suites numériques 0 analyse numérique, arithmétique, corrigé, mathematique, QCM, QCM analyse numérique, QCM calcul de somme, QCM convergence, QCM développement limité, qcm suites numeriques, séries, suites 17 h 44 <html xml:lang="en" xmlns="http://www.w3.org/1998/Math/MathML"> <head> <title>MathMagic Equation - www.mathmagic.com </title> <script src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_SVG" type="text/javascript"></script> </head> <body> <!-- MathMagic Pro Win v8.0, MathML 2.0 converter, 2015.6.15 08:08 --> <math xmlns="http://www.w3.org/1998/Math/MathML"> <semantics> <mstyle> <mtable> <mtr> <mtd columnalign="left"> <mi mathcolor="#0000ff" mathsize="17.0pt">QCM</mi> <mspace width="0.33em"> <mi mathcolor="#0000ff" mathsize="17.0pt">Suites</mi> <mspace width="0.33em"> <mi mathcolor="#0000ff" mathsize="17.0pt">n</mi> <mi mathcolor="#0000ff" mathsize="17.0pt">u</mi> <mi mathcolor="#0000ff" mathsize="17.0pt">m</mi> <mi mathcolor="#0000ff" 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</semantics> </math> </body> <div> <a href="https://docs.google.com/viewer?a=v&pid=sites&srcid=ZGVmYXVsdGRvbWFpbnxtYXRocWNtfGd4OjM5YTVlNmUwMTc4ODYxMzY"><b>TELECHARGER VERSION PDF</b></a></div> </html><br /> <div class="separator" style="clear: both; text-align: center;"> <a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhqtz5faxvOVESHI6S_wVyh46evOMtVUNMRBv0BxdwTKm99JA0UacnLIEtAt3WHPwAzIU4x1z0BCWgfXCwHdJlgeb64Hu7kGkfUOwr221AudAgxQhugyXMAADDWeDM6c_pdv2OuQyDHJ9Nw/s1600/q1.PNG" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhqtz5faxvOVESHI6S_wVyh46evOMtVUNMRBv0BxdwTKm99JA0UacnLIEtAt3WHPwAzIU4x1z0BCWgfXCwHdJlgeb64Hu7kGkfUOwr221AudAgxQhugyXMAADDWeDM6c_pdv2OuQyDHJ9Nw/s200/q1.PNG" /></a></div> QCM Suites numériques MathMagic Equation - www.mathmagic.com QCM ... 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