Quiz — TD2 Prob GLSI2 1+SEiot2.pdf

Question 1 sur 10 20:00

[{"id":11983,"question":"Quelle est la probabilité d'obtenir un '6' en lançant un dé équilibré ?","option_a":"1\/2","option_b":"1\/3","option_c":"1\/6","option_d":"1\/4","option_e":"","option_f":"","bonne_reponse":"c","explication":"Un dé équilibré a 6 faces, donc la probabilité d'obtenir un '6' est de 1\/6.","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\/2\", \"b\": \"1\/3\", \"c\": \"1\/6\", \"d\": \"1\/4\"}}","_debug_options_count":4},{"id":11984,"question":"La loi binomiale s'applique-t-elle à des expériences aléatoires répétées et indépendantes ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La loi binomiale modélise le nombre de succès dans une série d'expériences aléatoires indépendantes et identiques.","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":11985,"question":"Quelle est la formule de l'espérance mathématique d'une variable aléatoire discrète X ?","option_a":"E(X) = Σx·P(X=x)","option_b":"E(X) = ΣP(X=x)","option_c":"E(X) = Σx²·P(X=x)","option_d":"E(X) = ΣP(X=x)\/x","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'espérance mathématique est calculée en multipliant chaque valeur possible de X par sa probabilité, puis en sommant le tout.","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(X) = Σx·P(X=x)\", \"b\": \"E(X) = ΣP(X=x)\", \"c\": \"E(X) = Σx²·","_debug_options_count":4},{"id":11986,"question":"Si deux événements A et B sont indépendants, alors P(A∩B) = P(A) × P(B).","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Par définition, deux événements sont indépendants si et seulement 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\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":11987,"question":"Quelle est la variance d'une variable aléatoire suivant une loi binomiale B(n,p) ?","option_a":"n·p","option_b":"n·p·(1-p)","option_c":"p·(1-p)","option_d":"n²·p","option_e":"","option_f":"","bonne_reponse":"b","explication":"La variance d'une loi binomiale B(n,p) est donnée par la formule n·p·(1-p).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"n·p\", \"b\": \"n·p·(1-p)\", \"c\": \"p·(1-p)\", \"d\": \"n²·p\"}}","_debug_options_count":4},{"id":11988,"question":"La loi normale est-elle 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":11989,"question":"Que représente l'écart-type dans une série statistique ?","option_a":"La moyenne des valeurs","option_b":"La dispersion des valeurs autour de la moyenne","option_c":"Le nombre total de valeurs","option_d":"La valeur maximale de la série","option_e":"","option_f":"","bonne_reponse":"b","explication":"L'écart-type mesure la dispersion des valeurs autour de la moyenne dans une série statistique.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"La moyenne des valeurs\", \"b\": \"La dispersion des valeurs autour d","_debug_options_count":4},{"id":11990,"question":"Si P(A) = 0.4 et P(B) = 0.5, et que A et B sont incompatibles, alors P(A∪B) = ?","option_a":"0.2","option_b":"0.9","option_c":"0.1","option_d":"0.5","option_e":"","option_f":"","bonne_reponse":"b","explication":"Pour deux événements incompatibles, P(A∪B) = P(A) + P(B) = 0.4 + 0.5 = 0.9.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"0.2\", \"b\": \"0.9\", \"c\": \"0.1\", \"d\": \"0.5\"}}","_debug_options_count":4},{"id":11991,"question":"La médiane d'une série statistique est toujours égale à la moyenne.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La médiane et la moyenne sont égales uniquement si la série est symétrique. Sinon, elles peuvent différer.","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":11992,"question":"Quelle est la probabilité d'obtenir au moins un '6' en lançant deux dés équilibrés ?","option_a":"1\/6","option_b":"11\/36","option_c":"1\/12","option_d":"1\/2","option_e":"","option_f":"","bonne_reponse":"b","explication":"La probabilité d'obtenir au moins un '6' est de 1 - (5\/6)² = 11\/36.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"1\/6\", \"b\": \"11\/36\", \"c\": \"1\/12\", \"d\": \"1\/2\"}}","_debug_options_count":4}]