{"id":42,"date":"2018-07-20T11:44:10","date_gmt":"2018-07-20T09:44:10","guid":{"rendered":"http:\/\/mathquiz.fr\/?page_id=42"},"modified":"2018-07-25T14:49:14","modified_gmt":"2018-07-25T12:49:14","slug":"probabilite-conditionnelle","status":"publish","type":"page","link":"https:\/\/mathquiz.fr\/?page_id=42","title":{"rendered":"Probabilit\u00e9 conditionnelle"},"content":{"rendered":"<div id=\"mtq_quiz_area-1\" class=\"mtq_quiz_area mtq_color_blue\"> \r\n  <!--Quiz generated using mTouch Quiz Version 3.1.3 by G. Michael Guy (http:\/\/gmichaelguy.com\/quizplugin\/)-->\r\n        \r\n      \r\n  <!-- Shortcode entered mtouchquiz id=5 --> \r\n  <!-- Shortcode interpreted mtouchquiz id=5 alerts=on singlepage=on hints=off startscreen=on finalscreen=on multiplechances=off showanswers=now show_stamps=on randomq=on randoma=on status=on labels=on title=on proofread=off list=off time=off scoring=off formid= vform=on autoadvance=off autosubmit=off inform=off forcecf=off forcegf=off offset=1 questions=9 firstid=37 lastid=45 color=blue --> \r\n  <!--form action=\"\" method=\"post\" class=\"quiz-form\" id=\"quiz-5\"-->\r\n    <div id=\"mtq_quiztitle-1\" class=\"mtq_quiztitle\" >\r\n  <h2>Probabilit\u00e9 conditionelle<\/h2>\r\n  <\/div>\r\n      <noscript>\r\n  <div id=\"mtq_javawarning-1\" class=\"mtq_javawarning\">\r\n  Veuillez attendre la fin du chargement de l'activit\u00e9. <\/br>Si l'activit\u00e9 se ne charge pas, essayez de rafra\u00eechir votre navigateur. Cette page n\u00e9cessite aussi Javascript. Veuillez la visiter avec Javascript activ\u00e9.  <div class=\"mtq_failed_button\" onclick=\"mtq_start_one(1)\">\r\n  Si le chargement \u00e9choue, cliquez ici pour r\u00e9-essayer  <\/div><\/div>\r\n  <\/noscript>\r\n    <div id=\"mtq_instructions-1\" class=\"mtq_instructions\"><\/div> <div id=\"mtq_start_button-1\" class='mtq_action_button mtq_css_button mtq_start_button' onclick='mtq_start_quiz(1)'> <div class=\"mtq_start_text\">\r\n  D\u00e9part  <\/div> <\/div>\r\n  <div id=\"mtq_quiz_results_bubble-1\" class=\"mtq_quiz_results_bubble\"> <div id=\"mtq_quiz_results-1\" class=\"mtq_quiz_results\"><p>F\u00e9licitation - vous avez compl\u00e9t\u00e9 <em>Probabilit\u00e9 conditionelle<\/em>.<\/p><p>Vous avez obtenu  %%SCORE%% sur %%TOTAL%%.<\/p><p>Votre performance a \u00e9t\u00e9 \u00e9valu\u00e9e \u00e0 %%RATING%%<\/p> <br>    \r\n  <\/div> <div id=\"mtq_quiz_results_highlight-1\" class=\"mtq_quiz_results_highlight\">\r\n  Vos r\u00e9ponses sont surlign\u00e9es ci-dessous.  <\/div> <\/div>\r\n    \r\n  <!-- root element for mtqscrollable -->\r\n\r\n  <div id=\"mtq_question_container-1\" style='display:none'>\r\n  <div >\r\n          <div class='mtq_question mtq_scroll_item-1' id='mtq_question-1-1'><table class='mtq_question_heading_table'><tr><td><div class='mtq_question_label '>Question 1<\/div><div id='mtq_stamp-1-1' class='mtq_stamp'><\/div><\/td><\/tr><\/table><div id='mtq_question_text-1-1' class='mtq_question_text'>Soit <span class=\"wp-katex-eq\" data-display=\"false\">X<\/span> une variable al\u00e9atoire qui suit une loi binomiale <span class=\"wp-katex-eq\" data-display=\"false\">B(10;0,2)<\/span>. D\u00e9terminer la probabilit\u00e9 que <span class=\"wp-katex-eq\" data-display=\"false\">P(X\\leqslant 4)<\/span> (arrondie \u00e0 <span class=\"wp-katex-eq\" data-display=\"false\">10^{-3}<\/span>)<\/div><table class='mtq_answer_table'><colgroup><col class='mtq_oce_first'\/><\/colgroup><tr id='mtq_row-1-1-1' onclick='mtq_button_click(1,1,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-1-1-1' class='mtq_css_letter_button mtq_letter_button_0'  alt='Question 1, Choice 1'>A<\/div><div id='mtq_marker-1-1-1' class='mtq_marker mtq_correct_marker' alt='Correct'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-1-1-1' class='mtq_answer_text'>0,967<\/div><\/td><\/tr><tr id='mtq_row-1-2-1' onclick='mtq_button_click(1,2,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-1-2-1' class='mtq_css_letter_button mtq_letter_button_1'  alt='Question 1, Choice 2'>B<\/div><div id='mtq_marker-1-2-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-1-2-1' class='mtq_answer_text'>0,201<\/div><\/td><\/tr><tr id='mtq_row-1-3-1' onclick='mtq_button_click(1,3,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-1-3-1' class='mtq_css_letter_button mtq_letter_button_2'  alt='Question 1, Choice 3'>C<\/div><div id='mtq_marker-1-3-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-1-3-1' class='mtq_answer_text'>0,088<\/div><\/td><\/tr><tr id='mtq_row-1-4-1' onclick='mtq_button_click(1,4,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-1-4-1' class='mtq_css_letter_button mtq_letter_button_3'  alt='Question 1, Choice 4'>D<\/div><div id='mtq_marker-1-4-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-1-4-1' class='mtq_answer_text'>0,033<\/div><\/td><\/tr><\/table><div id='mtq_question_explanation-1-1' class='mtq_explanation'><div class='mtq_explanation-label'>Explication pour la question 1:&nbsp;<\/div><div class='mtq_explanation-text'> A la calculatrice, on calcule la probabilit\u00e9 avec BinominalCD(4,10,0.2) (voir p259 du manuel)<\/div><\/div><\/div><div class='mtq_question mtq_scroll_item-1' id='mtq_question-2-1'><table class='mtq_question_heading_table'><tr><td><div class='mtq_question_label '>Question 2<\/div><div id='mtq_stamp-2-1' class='mtq_stamp'><\/div><\/td><\/tr><\/table><div id='mtq_question_text-2-1' class='mtq_question_text'>Une entreprise sp\u00e9cialis\u00e9e dans la fabrication de confitures fait appel \u00e0 des producteurs locaux. \u00c0 la livraison, l\u2019entreprise\r\neffectue un contr\u00f4le qualit\u00e9 \u00e0 l\u2019issue duquel les fruits sont s\u00e9lectionn\u00e9s ou non pour la pr\u00e9paration des confitures.\r\nUne \u00e9tude statistique a \u00e9tabli que :\r\n\r\n\r\n\t<li> 22 % des fruits livr\u00e9s sont issus de l\u2019agriculture biologique ;<\/li>\r\n\r\n\t<li> parmi les fruits issus de l\u2019agriculture biologique, 95 % sont s\u00e9lectionn\u00e9s pour la pr\u00e9paration des confitures ;<\/li>\r\n\r\n\r\n\r\n\r\n\t<li> parmi les fruits non issus de l\u2019agriculture biologique, 90 % sont s\u00e9lectionn\u00e9s pour la pr\u00e9paration des confitures.<\/li>\r\n\r\n<ol>\r\n\r\n\r\n<ol>\r\nOn note <span class=\"wp-katex-eq\" data-display=\"false\">B<\/span> l'\u00e9v\u00e9nement : Les fruits livr\u00e9s sont issue de l'agriculture biologique.<\/ol>\r\n<ol>\r\n\r\n\r\n\r\nOn note <span class=\"wp-katex-eq\" data-display=\"false\">C<\/span> l'\u00e9v\u00e9nement : Les fruits livr\u00e9s sont s\u00e9lectionn\u00e9s pour la pr\u00e9paration des confitures.<\/ol><\/div><table class='mtq_answer_table'><colgroup><col class='mtq_oce_first'\/><\/colgroup><tr id='mtq_row-2-1-1' onclick='mtq_button_click(2,1,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-2-1-1' class='mtq_css_letter_button mtq_letter_button_0'  alt='Question 2, Choice 1'>A<\/div><div id='mtq_marker-2-1-1' class='mtq_marker mtq_correct_marker' alt='Correct'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-2-1-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">P(B \\cap C)=0,209<\/span><\/div><\/td><\/tr><tr id='mtq_row-2-2-1' onclick='mtq_button_click(2,2,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-2-2-1' class='mtq_css_letter_button mtq_letter_button_1'  alt='Question 2, Choice 2'>B<\/div><div id='mtq_marker-2-2-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-2-2-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">P(B \\cap C)=0,9<\/span><\/div><\/td><\/tr><tr id='mtq_row-2-3-1' onclick='mtq_button_click(2,3,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-2-3-1' class='mtq_css_letter_button mtq_letter_button_2'  alt='Question 2, Choice 3'>C<\/div><div id='mtq_marker-2-3-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-2-3-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">P(B \\cap C)=0,198<\/span><\/div><\/td><\/tr><tr id='mtq_row-2-4-1' onclick='mtq_button_click(2,4,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-2-4-1' class='mtq_css_letter_button mtq_letter_button_3'  alt='Question 2, Choice 4'>D<\/div><div id='mtq_marker-2-4-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-2-4-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">(B \\cap C)=0,95<\/span><\/div><\/td><\/tr><\/table><div id='mtq_question_explanation-2-1' class='mtq_explanation'><div class='mtq_explanation-label'>Explication pour la question 2:&nbsp;<\/div><div class='mtq_explanation-text'> <span class=\"wp-katex-eq\" data-display=\"false\">P(B \\cap C)=P(B)\\times P_B(C)=0,22\\times 0,95=0,209<\/span><\/div><\/div><\/div><div class='mtq_question mtq_scroll_item-1' id='mtq_question-3-1'><table class='mtq_question_heading_table'><tr><td><div class='mtq_question_label '>Question 3<\/div><div id='mtq_stamp-3-1' class='mtq_stamp'><\/div><\/td><\/tr><\/table><div id='mtq_question_text-3-1' class='mtq_question_text'>Soient <span class=\"wp-katex-eq\" data-display=\"false\">A<\/span> et <span class=\"wp-katex-eq\" data-display=\"false\">B<\/span> deux \u00e9v\u00e9nements d'une exp\u00e9rience al\u00e9atoire telle que <span class=\"wp-katex-eq\" data-display=\"false\">P(A)=0,2<\/span> et <span class=\"wp-katex-eq\" data-display=\"false\">P(A\\cap B)=0,15<\/span>. Alors :<\/div><table class='mtq_answer_table'><colgroup><col class='mtq_oce_first'\/><\/colgroup><tr id='mtq_row-3-1-1' onclick='mtq_button_click(3,1,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-3-1-1' class='mtq_css_letter_button mtq_letter_button_0'  alt='Question 3, Choice 1'>A<\/div><div id='mtq_marker-3-1-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-3-1-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">P_A(B)=1,3333333.....<\/span><\/div><\/td><\/tr><tr id='mtq_row-3-2-1' onclick='mtq_button_click(3,2,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-3-2-1' class='mtq_css_letter_button mtq_letter_button_1'  alt='Question 3, Choice 2'>B<\/div><div id='mtq_marker-3-2-1' class='mtq_marker mtq_correct_marker' alt='Correct'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-3-2-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">P_A(B)=0,75<\/span><\/div><\/td><\/tr><tr id='mtq_row-3-3-1' onclick='mtq_button_click(3,3,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-3-3-1' class='mtq_css_letter_button mtq_letter_button_2'  alt='Question 3, Choice 3'>C<\/div><div id='mtq_marker-3-3-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-3-3-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">P_A(B)=0,25<\/span><\/div><\/td><\/tr><tr id='mtq_row-3-4-1' onclick='mtq_button_click(3,4,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-3-4-1' class='mtq_css_letter_button mtq_letter_button_3'  alt='Question 3, Choice 4'>D<\/div><div id='mtq_marker-3-4-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-3-4-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">P_A(B)=1<\/span><\/div><\/td><\/tr><\/table><div id='mtq_question_explanation-3-1' class='mtq_explanation'><div class='mtq_explanation-label'>Explication pour la question 3:&nbsp;<\/div><div class='mtq_explanation-text'> (cf d\u00e9finition 11) <span class=\"wp-katex-eq\" data-display=\"false\">P_A(B)=\\dfrac{P(A\\cap B)}{P(A)}=\\dfrac{0,15}{0,2}=0,75<\/span><\/div><\/div><\/div><div class='mtq_question mtq_scroll_item-1' id='mtq_question-4-1'><table class='mtq_question_heading_table'><tr><td><div class='mtq_question_label '>Question 4<\/div><div id='mtq_stamp-4-1' class='mtq_stamp'><\/div><\/td><\/tr><\/table><div id='mtq_question_text-4-1' class='mtq_question_text'>Soit <span class=\"wp-katex-eq\" data-display=\"false\">X<\/span> une variable al\u00e9atoire qui suit une loi binomiale <span class=\"wp-katex-eq\" data-display=\"false\">B(10;0,2)<\/span>. D\u00e9terminer la probabilit\u00e9 que <span class=\"wp-katex-eq\" data-display=\"false\">P(X=3)<\/span> (arrondie \u00e0 <span class=\"wp-katex-eq\" data-display=\"false\">10^{-3}<\/span>)<\/div><table class='mtq_answer_table'><colgroup><col class='mtq_oce_first'\/><\/colgroup><tr id='mtq_row-4-1-1' onclick='mtq_button_click(4,1,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-4-1-1' class='mtq_css_letter_button mtq_letter_button_0'  alt='Question 4, Choice 1'>A<\/div><div id='mtq_marker-4-1-1' class='mtq_marker mtq_correct_marker' alt='Correct'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-4-1-1' class='mtq_answer_text'>0,201<\/div><\/td><\/tr><tr id='mtq_row-4-2-1' onclick='mtq_button_click(4,2,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-4-2-1' class='mtq_css_letter_button mtq_letter_button_1'  alt='Question 4, Choice 2'>B<\/div><div id='mtq_marker-4-2-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-4-2-1' class='mtq_answer_text'>0,088<\/div><\/td><\/tr><tr id='mtq_row-4-3-1' onclick='mtq_button_click(4,3,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-4-3-1' class='mtq_css_letter_button mtq_letter_button_2'  alt='Question 4, Choice 3'>C<\/div><div id='mtq_marker-4-3-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-4-3-1' class='mtq_answer_text'>0,967<\/div><\/td><\/tr><tr id='mtq_row-4-4-1' onclick='mtq_button_click(4,4,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-4-4-1' class='mtq_css_letter_button mtq_letter_button_3'  alt='Question 4, Choice 4'>D<\/div><div id='mtq_marker-4-4-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-4-4-1' class='mtq_answer_text'>0,033<\/div><\/td><\/tr><\/table><div id='mtq_question_explanation-4-1' class='mtq_explanation'><div class='mtq_explanation-label'>Explication pour la question 4:&nbsp;<\/div><div class='mtq_explanation-text'> A la calculatrice, on calcule la probabilit\u00e9 avec BinominalPD(3,10,0.2) (voir p259 du manuel)<\/div><\/div><\/div><div class='mtq_question mtq_scroll_item-1' id='mtq_question-5-1'><table class='mtq_question_heading_table'><tr><td><div class='mtq_question_label '>Question 5<\/div><div id='mtq_stamp-5-1' class='mtq_stamp'><\/div><\/td><\/tr><\/table><div id='mtq_question_text-5-1' class='mtq_question_text'>Soit <span class=\"wp-katex-eq\" data-display=\"false\">X<\/span> une variable al\u00e9atoire qui suit une loi binomiale <span class=\"wp-katex-eq\" data-display=\"false\">B(10;0,2)<\/span>, alors :<\/div><table class='mtq_answer_table'><colgroup><col class='mtq_oce_first'\/><\/colgroup><tr id='mtq_row-5-1-1' onclick='mtq_button_click(5,1,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-5-1-1' class='mtq_css_letter_button mtq_letter_button_0'  alt='Question 5, Choice 1'>A<\/div><div id='mtq_marker-5-1-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-5-1-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">E(X)=10<\/span><\/div><\/td><\/tr><tr id='mtq_row-5-2-1' onclick='mtq_button_click(5,2,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-5-2-1' class='mtq_css_letter_button mtq_letter_button_1'  alt='Question 5, Choice 2'>B<\/div><div id='mtq_marker-5-2-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-5-2-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">E(X)=0,2<\/span><\/div><\/td><\/tr><tr id='mtq_row-5-3-1' onclick='mtq_button_click(5,3,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-5-3-1' class='mtq_css_letter_button mtq_letter_button_2'  alt='Question 5, Choice 3'>C<\/div><div id='mtq_marker-5-3-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-5-3-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">E(X)=5<\/span><\/div><\/td><\/tr><tr id='mtq_row-5-4-1' onclick='mtq_button_click(5,4,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-5-4-1' class='mtq_css_letter_button mtq_letter_button_3'  alt='Question 5, Choice 4'>D<\/div><div id='mtq_marker-5-4-1' class='mtq_marker mtq_correct_marker' alt='Correct'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-5-4-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">E(X)=2<\/span><\/div><\/td><\/tr><\/table><div id='mtq_question_explanation-5-1' class='mtq_explanation'><div class='mtq_explanation-label'>Explication pour la question 5:&nbsp;<\/div><div class='mtq_explanation-text'> (cf propri\u00e9t\u00e9 1) <span class=\"wp-katex-eq\" data-display=\"false\">E(X)=np=10\\times 0,2=2<\/span><\/div><\/div><\/div><div class='mtq_question mtq_scroll_item-1' id='mtq_question-6-1'><table class='mtq_question_heading_table'><tr><td><div class='mtq_question_label '>Question 6<\/div><div id='mtq_stamp-6-1' class='mtq_stamp'><\/div><\/td><\/tr><\/table><div id='mtq_question_text-6-1' class='mtq_question_text'>Soient <span class=\"wp-katex-eq\" data-display=\"false\">A<\/span> et <span class=\"wp-katex-eq\" data-display=\"false\">B<\/span> deux \u00e9v\u00e9nements d'une exp\u00e9rience al\u00e9atoire telle que <span class=\"wp-katex-eq\" data-display=\"false\">P(A)=0,2<\/span> et <span class=\"wp-katex-eq\" data-display=\"false\">P_A(B)=0,15<\/span>. Alors :<\/div><table class='mtq_answer_table'><colgroup><col class='mtq_oce_first'\/><\/colgroup><tr id='mtq_row-6-1-1' onclick='mtq_button_click(6,1,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-6-1-1' class='mtq_css_letter_button mtq_letter_button_0'  alt='Question 6, Choice 1'>A<\/div><div id='mtq_marker-6-1-1' class='mtq_marker mtq_correct_marker' alt='Correct'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-6-1-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">P(A\\cap B)=0,03<\/span><\/div><\/td><\/tr><tr id='mtq_row-6-2-1' onclick='mtq_button_click(6,2,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-6-2-1' class='mtq_css_letter_button mtq_letter_button_1'  alt='Question 6, Choice 2'>B<\/div><div id='mtq_marker-6-2-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-6-2-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">P(A\\cap B)=0,75<\/span><\/div><\/td><\/tr><tr id='mtq_row-6-3-1' onclick='mtq_button_click(6,3,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-6-3-1' class='mtq_css_letter_button mtq_letter_button_2'  alt='Question 6, Choice 3'>C<\/div><div id='mtq_marker-6-3-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-6-3-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">P(A\\cap B)=1<\/span><\/div><\/td><\/tr><tr id='mtq_row-6-4-1' onclick='mtq_button_click(6,4,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-6-4-1' class='mtq_css_letter_button mtq_letter_button_3'  alt='Question 6, Choice 4'>D<\/div><div id='mtq_marker-6-4-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-6-4-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">P(A\\cap B)=1,333333.....<\/span><\/div><\/td><\/tr><\/table><div id='mtq_question_explanation-6-1' class='mtq_explanation'><div class='mtq_explanation-label'>Explication pour la question 6:&nbsp;<\/div><div class='mtq_explanation-text'> (cf propri\u00e9t\u00e9 5) <span class=\"wp-katex-eq\" data-display=\"false\">P(A\\cap B)=P(A)\\times P_A(B)=0,2\\times 0,15= 0,03<\/span><\/div><\/div><\/div><div class='mtq_question mtq_scroll_item-1' id='mtq_question-7-1'><table class='mtq_question_heading_table'><tr><td><div class='mtq_question_label '>Question 7<\/div><div id='mtq_stamp-7-1' class='mtq_stamp'><\/div><\/td><\/tr><\/table><div id='mtq_question_text-7-1' class='mtq_question_text'>Soit <span class=\"wp-katex-eq\" data-display=\"false\">X<\/span> une variable al\u00e9atoire qui suit une loi binomiale <span class=\"wp-katex-eq\" data-display=\"false\">B(10;0,2)<\/span>. D\u00e9terminer la probabilit\u00e9 que <span class=\"wp-katex-eq\" data-display=\"false\">P(X&gt;4)<\/span> (arrondie \u00e0 <span class=\"wp-katex-eq\" data-display=\"false\">10^{-3}<\/span>)<\/div><table class='mtq_answer_table'><colgroup><col class='mtq_oce_first'\/><\/colgroup><tr id='mtq_row-7-1-1' onclick='mtq_button_click(7,1,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-7-1-1' class='mtq_css_letter_button mtq_letter_button_0'  alt='Question 7, Choice 1'>A<\/div><div id='mtq_marker-7-1-1' class='mtq_marker mtq_correct_marker' alt='Correct'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-7-1-1' class='mtq_answer_text'>0,033<\/div><\/td><\/tr><tr id='mtq_row-7-2-1' onclick='mtq_button_click(7,2,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-7-2-1' class='mtq_css_letter_button mtq_letter_button_1'  alt='Question 7, Choice 2'>B<\/div><div id='mtq_marker-7-2-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-7-2-1' class='mtq_answer_text'>0,967<\/div><\/td><\/tr><tr id='mtq_row-7-3-1' onclick='mtq_button_click(7,3,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-7-3-1' class='mtq_css_letter_button mtq_letter_button_2'  alt='Question 7, Choice 3'>C<\/div><div id='mtq_marker-7-3-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-7-3-1' class='mtq_answer_text'>0,088<\/div><\/td><\/tr><tr id='mtq_row-7-4-1' onclick='mtq_button_click(7,4,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-7-4-1' class='mtq_css_letter_button mtq_letter_button_3'  alt='Question 7, Choice 4'>D<\/div><div id='mtq_marker-7-4-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-7-4-1' class='mtq_answer_text'>0,201<\/div><\/td><\/tr><\/table><div id='mtq_question_explanation-7-1' class='mtq_explanation'><div class='mtq_explanation-label'>Explication pour la question 7:&nbsp;<\/div><div class='mtq_explanation-text'> A la calculatrice, on calcule la probabilit\u00e9 avec 1-BinominalCD(4,10,0.2). Car <span class=\"wp-katex-eq\" data-display=\"false\">P(X&gt;4)=1-P(X\\leqslant 4)<\/span> (voir p259 du manuel)<\/div><\/div><\/div><div class='mtq_question mtq_scroll_item-1' id='mtq_question-8-1'><table class='mtq_question_heading_table'><tr><td><div class='mtq_question_label '>Question 8<\/div><div id='mtq_stamp-8-1' class='mtq_stamp'><\/div><\/td><\/tr><\/table><div id='mtq_question_text-8-1' class='mtq_question_text'>Une entreprise sp\u00e9cialis\u00e9e dans la fabrication de confitures fait appel \u00e0 des producteurs locaux. \u00c0 la livraison, l\u2019entreprise\r\neffectue un contr\u00f4le qualit\u00e9 \u00e0 l\u2019issue duquel les fruits sont s\u00e9lectionn\u00e9s ou non pour la pr\u00e9paration des confitures.\r\nUne \u00e9tude statistique a \u00e9tabli que :\r\n\r\n\r\n\t<li> 22 % des fruits livr\u00e9s sont issus de l\u2019agriculture biologique ;<\/li>\r\n\r\n\t<li> parmi les fruits issus de l\u2019agriculture biologique, 95 % sont s\u00e9lectionn\u00e9s pour la pr\u00e9paration des confitures ;<\/li>\r\n\r\n\r\n\r\n\r\n\t<li> parmi les fruits non issus de l\u2019agriculture biologique, 90 % sont s\u00e9lectionn\u00e9s pour la pr\u00e9paration des confitures.<\/li>\r\n\r\n<ol>\r\n\r\n\r\n<ol>\r\nOn note <span class=\"wp-katex-eq\" data-display=\"false\">B<\/span> l'\u00e9v\u00e9nement : Les fruits livr\u00e9s sont issue de l'agriculture biologique.<\/ol>\r\n<ol>\r\n\r\n\r\n\r\nOn note <span class=\"wp-katex-eq\" data-display=\"false\">C<\/span> l'\u00e9v\u00e9nement : Les fruits livr\u00e9s sont s\u00e9lectionn\u00e9s pour la pr\u00e9paration des confitures.<\/ol>\r\n\r\n<\/div><table class='mtq_answer_table'><colgroup><col class='mtq_oce_first'\/><\/colgroup><tr id='mtq_row-8-1-1' onclick='mtq_button_click(8,1,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-8-1-1' class='mtq_css_letter_button mtq_letter_button_0'  alt='Question 8, Choice 1'>A<\/div><div id='mtq_marker-8-1-1' class='mtq_marker mtq_correct_marker' alt='Correct'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-8-1-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">P_{\\overline{B}}(C)=0,9<\/span><\/div><\/td><\/tr><tr id='mtq_row-8-2-1' onclick='mtq_button_click(8,2,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-8-2-1' class='mtq_css_letter_button mtq_letter_button_1'  alt='Question 8, Choice 2'>B<\/div><div id='mtq_marker-8-2-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-8-2-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">P_{\\overline{B}}(C)=0,209<\/span><\/div><\/td><\/tr><tr id='mtq_row-8-3-1' onclick='mtq_button_click(8,3,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-8-3-1' class='mtq_css_letter_button mtq_letter_button_2'  alt='Question 8, Choice 3'>C<\/div><div id='mtq_marker-8-3-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-8-3-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">P_{\\overline{B}}(C)=0,198<\/span><\/div><\/td><\/tr><tr id='mtq_row-8-4-1' onclick='mtq_button_click(8,4,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-8-4-1' class='mtq_css_letter_button mtq_letter_button_3'  alt='Question 8, Choice 4'>D<\/div><div id='mtq_marker-8-4-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-8-4-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">P_{\\overline{B}}(C)=0,95<\/span><\/div><\/td><\/tr><\/table><div id='mtq_question_explanation-8-1' class='mtq_explanation'><div class='mtq_explanation-label'>Explication pour la question 8:&nbsp;<\/div><div class='mtq_explanation-text'> La r\u00e9ponse est dans l'\u00e9nonc\u00e9 : \"parmi les fruits non issus de l\u2019agriculture biologique, 90 % sont s\u00e9lectionn\u00e9s pour la pr\u00e9paration des confitures.\"<\/div><\/div><\/div><div class='mtq_question mtq_scroll_item-1' id='mtq_question-9-1'><table class='mtq_question_heading_table'><tr><td><div class='mtq_question_label '>Question 9<\/div><div id='mtq_stamp-9-1' class='mtq_stamp'><\/div><\/td><\/tr><\/table><div id='mtq_question_text-9-1' class='mtq_question_text'><img src=\"http:\/\/mathquiz.fr\/wp-content\/uploads\/2018\/07\/rep7.png\" alt=\"\" width=\"201\" height=\"165\" class=\"alignnone size-full wp-image-132\" \/>\r\n\r\n<ol>\r\n<\/ol>\r\n\r\nA partir de l'arbre pond\u00e9r\u00e9 pr\u00e9sent\u00e9 ci-dessus, d\u00e9terminer <span class=\"wp-katex-eq\" data-display=\"false\">P(D)<\/span>.<\/div><table class='mtq_answer_table'><colgroup><col class='mtq_oce_first'\/><\/colgroup><tr id='mtq_row-9-1-1' onclick='mtq_button_click(9,1,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-9-1-1' class='mtq_css_letter_button mtq_letter_button_0'  alt='Question 9, Choice 1'>A<\/div><div id='mtq_marker-9-1-1' class='mtq_marker mtq_correct_marker' alt='Correct'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-9-1-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">P(D)=0,236<\/span><\/div><\/td><\/tr><tr id='mtq_row-9-2-1' onclick='mtq_button_click(9,2,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-9-2-1' class='mtq_css_letter_button mtq_letter_button_1'  alt='Question 9, Choice 2'>B<\/div><div id='mtq_marker-9-2-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-9-2-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">P(D)=0,05<\/span><\/div><\/td><\/tr><tr id='mtq_row-9-3-1' onclick='mtq_button_click(9,3,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-9-3-1' class='mtq_css_letter_button mtq_letter_button_2'  alt='Question 9, Choice 3'>C<\/div><div id='mtq_marker-9-3-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-9-3-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">P(D)=0,98<\/span><\/div><\/td><\/tr><tr id='mtq_row-9-4-1' onclick='mtq_button_click(9,4,1)' class='mtq_clickable'><td class='mtq_letter_button_td'><div id='mtq_button-9-4-1' class='mtq_css_letter_button mtq_letter_button_3'  alt='Question 9, Choice 4'>D<\/div><div id='mtq_marker-9-4-1' class='mtq_marker mtq_wrong_marker' alt='Faux'><\/div><\/td><td class='mtq_answer_td'><div id='mtq_answer_text-9-4-1' class='mtq_answer_text'><span class=\"wp-katex-eq\" data-display=\"false\">P(D)=0,123<\/span><\/div><\/td><\/tr><\/table><div id='mtq_question_explanation-9-1' class='mtq_explanation'><div class='mtq_explanation-label'>Explication pour la question 9:&nbsp;<\/div><div class='mtq_explanation-text'> <span class=\"wp-katex-eq\" data-display=\"false\">D\\cap T<\/span> et <span class=\"wp-katex-eq\" data-display=\"false\">D\\cap \\overline{T}<\/span> sont disjoints. D'apr\u00e8s la formule des probabilit\u00e9s totales,  <span class=\"wp-katex-eq\" data-display=\"false\">P(D)=P(T \\cap D)+P(\\overline{T} \\cap D)=P(T)P_T(D)+P({\\overline{T}})P_{\\overline{T}}(D)=0,8\\times 0,05 + 0,2 \\times 0,98=0,236 <\/span>. (cf propri\u00e9t\u00e9 6 et 5 + exemple 9) <\/div><\/div><\/div>            <div id=\"mtq_results_request-1\" class=\"mtq_results_request mtq_scroll_item-1\">\r\n        Une fois termin\u00e9, cliquez sur le bouton ci-dessous. Toutes les questions que vous n'avez pas compl\u00e9t\u00e9es sont marqu\u00e9es comme incorrectes.        <span id=\"mtq_results_button-1\" class='mtq_action_button mtq_css_button mtq_results_button'  onclick='mtq_get_results(1)'> <span class=\"mtq_results_text\">\r\n        Obtenir les r\u00e9sultats        <\/span> <\/span> <\/div>\r\n                <!--End of mtqscrollable items--> \r\n    \r\n  <\/div>\r\n  <!--End of mtqscrollable--> \r\n  <!--mtq_status-->\r\n    <div id=\"mtq_quiz_status-1\" class=\"mtq_quiz_status\">\r\n  Il y a 9 questions \u00e0 compl\u00e9ter.  <\/div>\r\n      <\/div> \r\n  <!--Holds all questions-->\r\n    <div id=\"mtq_variables\" class=\"mtq_preload\" style=\"display:none\"> <input type='hidden' id='mtq_id-1' name='mtq_id_value' value='1' \/><input type='hidden' name='question_id[]' value='38'\/><input type='hidden' id='mtq_is_answered-1-1' value='0'\/><input type='hidden' id='mtq_is_correct-1-1' value='0'\/><input type='hidden' id='mtq_is_worth-1-1' 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id='mtq_is_correct-9-2-1' value='0'\/><input type='hidden' id='mtq_was_selected-9-2-1' value='0'\/><input type='hidden' id='mtq_was_ever_selected-9-2-1' value='0'\/><input type='hidden' id='mtq_has_hint-9-2-1' value='0'\/><input type='hidden' id='mtq_is_correct-9-3-1' value='0'\/><input type='hidden' id='mtq_was_selected-9-3-1' value='0'\/><input type='hidden' id='mtq_was_ever_selected-9-3-1' value='0'\/><input type='hidden' id='mtq_has_hint-9-3-1' value='0'\/><input type='hidden' id='mtq_is_correct-9-4-1' value='0'\/><input type='hidden' id='mtq_was_selected-9-4-1' value='0'\/><input type='hidden' id='mtq_was_ever_selected-9-4-1' value='0'\/><input type='hidden' id='mtq_has_hint-9-4-1' value='0'\/><input type='hidden' id='mtq_num_ans-9-1' value='4' \/><input type='hidden' id='mtq_num_correct-9-1' value='1' \/> <div id=\"mtq_have_completed_string\" class=\"mtq_preload\">\r\n    Vous avez compl\u00e9t\u00e9    <\/div> <div id=\"mtq_questions_string\" class=\"mtq_preload\">\r\n    questions    <\/div> <div id=\"mtq_question_string\" class=\"mtq_preload\">\r\n    question    <\/div> <div id=\"mtq_your_score_is_string\"  class=\"mtq_preload\">\r\n    Votre score est de    <\/div> <div id=\"mtq_correct_string\"  class=\"mtq_preload\">\r\n    Correct    <\/div> <div id=\"mtq_wrong_string\"  class=\"mtq_preload\">\r\n    Faux    <\/div> <div id=\"mtq_partial_string\"  class=\"mtq_preload\">\r\n    R\u00e9ponse partielle    <\/div> <div id=\"mtq_exit_warning_string\"  class=\"mtq_preload\">\r\n    Vous n'avez pas fini votre quiz. Si vous quittez cette page, votre progression sera perdue.    <\/div> <div id='mtq_correct_answer_string' class='mtq_preload'>\r\n    R\u00e9ponses correctes    <\/div> <div id='mtq_you_selected_string' class='mtq_preload'>\r\n    Vous avez s\u00e9lectionn\u00e9    <\/div> <div id='mtq_not_attempted_string' class='mtq_preload'>\r\n    Pas essayer    <\/div> <div id='mtq_final_score_on_quiz_string' class='mtq_preload'>\r\n    Score final du quiz    <\/div> <div id='mtq_attempted_questions_correct_string' class='mtq_preload'>\r\n    Nombre de questions r\u00e9pondues de mani\u00e8re correcte    <\/div> <div id='mtq_attempted_questions_wrong_string' class='mtq_preload'>\r\n    Nombre de questions r\u00e9pondues de mani\u00e8re incorrecte    <\/div> <div id='mtq_questions_not_attempted_string' class='mtq_preload'>\r\n    Question non r\u00e9pondues    <\/div> <div id='mtq_total_questions_on_quiz_string' class='mtq_preload'>\r\n    Nombre total de questions dans le quiz    <\/div> <div 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