Quiz — Probabilite.pdf

Question 1 sur 10 20:00

[{"id":4586,"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, chacune ayant la même probabilité d'apparaître. La probabilité d'obtenir un 6 est donc 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":4587,"question":"Deux événements A et B sont incompatibles si...","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Deux événements sont incompatibles s'ils ne peuvent pas se produire simultanément, c'est-à-dire si leur intersection est vide.","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":4588,"question":"Quelle formule permet de calculer la probabilité de l'union de deux événements A et B ?","option_a":"P(A) + P(B)","option_b":"P(A) + P(B) - P(A ∩ B)","option_c":"P(A) × P(B)","option_d":"P(A) \/ P(B)","option_e":"","option_f":"","bonne_reponse":"b","explication":"La formule de l'union de deux événements est P(A ∪ B) = P(A) + P(B) - P(A ∩ B), car on soustrait la probabilité de leur intersection pour éviter le double comptage.","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) - P(A ∩ B)\", \"c\": \"P(A) × P(B)","_debug_options_count":4},{"id":4589,"question":"La loi binomiale s'applique à des expériences...","option_a":"à issues continues","option_b":"à deux issues","option_c":"à trois issues","option_d":"à issues aléatoires","option_e":"","option_f":"","bonne_reponse":"b","explication":"La loi binomiale modélise des expériences à deux issues possibles (succès ou échec), comme lancer une pièce ou tirer une carte.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"à issues continues\", \"b\": \"à deux issues\", \"c\": \"à trois issue","_debug_options_count":4},{"id":4590,"question":"Quelle est la probabilité d'obtenir deux fois pile en deux lancers d'une pièce équilibrée ?","option_a":"1\/2","option_b":"1\/4","option_c":"1\/3","option_d":"1\/8","option_e":"","option_f":"","bonne_reponse":"b","explication":"La probabilité d'obtenir pile en un lancer est de 1\/2. Pour deux lancers indépendants, la probabilité est (1\/2) × (1\/2) = 1\/4.","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\/2\", \"b\": \"1\/4\", \"c\": \"1\/3\", \"d\": \"1\/8\"}}","_debug_options_count":4},{"id":4591,"question":"La moyenne d'une série statistique est toujours égale à la médiane.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La moyenne et la médiane sont des mesures de tendance centrale, mais elles ne sont pas toujours égales. Cela dépend de la distribution des données.","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":4592,"question":"Quelle est la probabilité de tirer un as dans un jeu de 52 cartes ?","option_a":"1\/13","option_b":"1\/4","option_c":"1\/52","option_d":"1\/26","option_e":"","option_f":"","bonne_reponse":"a","explication":"Un jeu de 52 cartes contient 4 as. La probabilité de tirer un as est donc de 4\/52 = 1\/13.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"1\/13\", \"b\": \"1\/4\", \"c\": \"1\/52\", \"d\": \"1\/26\"}}","_debug_options_count":4},{"id":4593,"question":"Dans une loi normale centrée réduite, quelle est la probabilité qu'une variable aléatoire X soit comprise entre -1 et 1 ?","option_a":"68%","option_b":"95%","option_c":"99%","option_d":"50%","option_e":"","option_f":"","bonne_reponse":"a","explication":"Dans une loi normale centrée réduite, environ 68% des valeurs se situent entre -1 et 1 écarts-types de la moyenne.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"68%\", \"b\": \"95%\", \"c\": \"99%\", \"d\": \"50%\"}}","_debug_options_count":4},{"id":4594,"question":"Deux événements A et B sont indépendants si...","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Deux événements sont indépendants si la réalisation de l'un n'influence pas la probabilité de l'autre, c'est-à-dire 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":4595,"question":"Quelle est la probabilité de ne pas obtenir un 5 en lançant un dé équilibré ?","option_a":"1\/6","option_b":"5\/6","option_c":"2\/3","option_d":"1\/2","option_e":"","option_f":"","bonne_reponse":"b","explication":"La probabilité d'obtenir un 5 est de 1\/6. La probabilité de ne pas obtenir un 5 est donc de 1 - 1\/6 = 5\/6.","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\": \"5\/6\", \"c\": \"2\/3\", \"d\": \"1\/2\"}}","_debug_options_count":4}]