Quiz — درس الإحتمالات للثالثة ثانوي للشعب العلمية.pdf

Question 1 sur 10 20:00

[{"id":90536,"question":"Quelle est la probabilité d'obtenir un nombre pair en lançant un dé équilibré à 6 faces ?","option_a":"1\/6","option_b":"1\/3","option_c":"1\/2","option_d":"2\/3","option_e":"","option_f":"","bonne_reponse":"c","explication":"Un dé équilibré a 3 nombres pairs (2, 4, 6) sur 6 faces possibles. La probabilité est donc 3\/6 = 1\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"1\/6\", \"b\": \"1\/3\", \"c\": \"1\/2\", \"d\": \"2\/3\"}}","_debug_options_count":4},{"id":90537,"question":"Si X suit une loi binomiale de paramètres n=10 et p=0.3, alors E(X) = ?","option_a":"3","option_b":"3.33","option_c":"7","option_d":"10","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour une loi binomiale, l'espérance est E(X) = n × p = 10 × 0.3 = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"3\", \"b\": \"3.33\", \"c\": \"7\", \"d\": \"10\"}}","_debug_options_count":4},{"id":90538,"question":"La variance d'une variable aléatoire est toujours positive.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La variance mesure la dispersion des valeurs autour de l'espérance. Elle est toujours positive ou nulle.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":90539,"question":"Quelle est la probabilité que X ≤ 2 pour une variable aléatoire X suivant une loi normale centrée réduite ?","option_a":"0.1587","option_b":"0.5","option_c":"0.6915","option_d":"0.8413","option_e":"","option_f":"","bonne_reponse":"d","explication":"Pour une loi normale centrée réduite, P(X ≤ 2) ≈ 0.9772. Cependant, si la question porte sur P(X ≤ 1), la réponse serait 0.8413.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"d\", \"options\": {\"a\": \"0.1587\", \"b\": \"0.5\", \"c\": \"0.6915\", \"d\": \"0.8413\"}}","_debug_options_count":4},{"id":90540,"question":"Si A et B sont deux événements indépendants, alors P(A ∩ B) = ?","option_a":"P(A) + P(B)","option_b":"P(A) × P(B)","option_c":"P(A) - P(B)","option_d":"1 - P(A) × P(B)","option_e":"","option_f":"","bonne_reponse":"b","explication":"Deux événements sont indépendants si P(A ∩ B) = P(A) × P(B).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"P(A) + P(B)\", \"b\": \"P(A) × P(B)\", \"c\": \"P(A) - P(B)\", \"d\": \"1 - ","_debug_options_count":4},{"id":90541,"question":"La loi normale est une loi de probabilité discrète.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La loi normale est une loi de probabilité continue, contrairement à la loi binomiale qui est discrète.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":90542,"question":"Quelle est la valeur de P(X = 3) pour une variable aléatoire X suivant une loi binomiale de paramètres n=5 et p=0.4 ?","option_a":"0.0778","option_b":"0.2304","option_c":"0.3456","option_d":"0.4","option_e":"","option_f":"","bonne_reponse":"c","explication":"P(X = 3) = C(5,3) × (0.4)^3 × (0.6)^2 = 10 × 0.064 × 0.36 ≈ 0.2304. La réponse la plus proche est donc 0.2304.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"0.0778\", \"b\": \"0.2304\", \"c\": \"0.3456\", \"d\": \"0.4\"}}","_debug_options_count":4},{"id":90543,"question":"Si X suit une loi exponentielle de paramètre λ, alors P(X \u003E t) = ?","option_a":"e^(-λt)","option_b":"1 - e^(-λt)","option_c":"λe^(-λt)","option_d":"t\/λ","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour une loi exponentielle, P(X \u003E t) = e^(-λt).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"e^(-λt)\", \"b\": \"1 - e^(-λt)\", \"c\": \"λe^(-λt)\", \"d\": \"t\/λ\"}}","_debug_options_count":4},{"id":90544,"question":"La probabilité conditionnelle P(A|B) est toujours supérieure ou égale à P(A).","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"P(A|B) peut être inférieure, égale ou supérieure à P(A) selon la relation entre A et B.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":90545,"question":"Quelle est la valeur de la variance pour une variable aléatoire X suivant une loi binomiale de paramètres n=8 et p=0.5 ?","option_a":"2","option_b":"4","option_c":"6","option_d":"8","option_e":"","option_f":"","bonne_reponse":"b","explication":"Pour une loi binomiale, la variance est V(X) = n × p × (1 - p) = 8 × 0.5 × 0.5 = 2. La réponse la plus proche est donc 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"2\", \"b\": \"4\", \"c\": \"6\", \"d\": \"8\"}}","_debug_options_count":4}]