Quiz — تمرين في الاحتمالات مرفق بالتصحيح.pdf - Master PDF Editor.pdf

Question 1 sur 10 20:00

[{"id":4736,"question":"Quelle est la probabilité de tirer un as dans un jeu de 52 cartes bien mélangé ?","option_a":"1\/13","option_b":"1\/52","option_c":"4\/52","option_d":"1\/4","option_e":"","option_f":"","bonne_reponse":"c","explication":"Un jeu de 52 cartes contient 4 as. La probabilité est donc de 4\/52, soit 1\/13.","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\/13\", \"b\": \"1\/52\", \"c\": \"4\/52\", \"d\": \"1\/4\"}}","_debug_options_count":4},{"id":4737,"question":"Si A et B sont deux événements 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":"Cette affirmation est vraie par définition de l'indépendance entre deux événements.","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":4738,"question":"Quelle loi de probabilité modélise le nombre de succès dans une série d'essais indépendants avec une probabilité de succès constante ?","option_a":"Loi uniforme","option_b":"Loi binomiale","option_c":"Loi exponentielle","option_d":"Loi de Poisson","option_e":"","option_f":"","bonne_reponse":"b","explication":"La loi binomiale modélise le nombre de succès dans une série d'essais indépendants avec une probabilité de succès constante 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\": \"Loi uniforme\", \"b\": \"Loi binomiale\", \"c\": \"Loi exponentielle\", \"d","_debug_options_count":4},{"id":4739,"question":"Dans une classe de 30 élèves, 12 sont des filles. Quelle est la probabilité de choisir une fille au hasard ?","option_a":"0.4","option_b":"0.3","option_c":"0.6","option_d":"0.25","option_e":"","option_f":"","bonne_reponse":"b","explication":"La probabilité est de 12\/30, soit 0.4 ou 40%.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"0.4\", \"b\": \"0.3\", \"c\": \"0.6\", \"d\": \"0.25\"}}","_debug_options_count":4},{"id":4740,"question":"La probabilité conditionnelle P(A|B) est toujours inférieure ou égale à P(A).","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Faux. P(A|B) peut être supérieure à P(A) si B favorise l'événement A.","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":4741,"question":"Quelle est la probabilité d'obtenir un double 6 en lançant deux dés équilibrés ?","option_a":"1\/6","option_b":"1\/36","option_c":"1\/12","option_d":"1\/18","option_e":"","option_f":"","bonne_reponse":"b","explication":"Il y a 36 combinaisons possibles avec deux dés. Une seule donne un double 6, donc la probabilité est de 1\/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\": \"1\/36\", \"c\": \"1\/12\", \"d\": \"1\/18\"}}","_debug_options_count":4},{"id":4742,"question":"Si P(A) = 0.7 et P(B) = 0.5, et si A et B sont incompatibles, alors P(A ∪ B) = ?","option_a":"0.35","option_b":"1.2","option_c":"0.85","option_d":"0.2","option_e":"","option_f":"","bonne_reponse":"c","explication":"Pour des événements incompatibles, P(A ∪ B) = P(A) + P(B) = 0.7 + 0.5 = 1.2. Cependant, une probabilité ne peut pas dépasser 1, donc cette situation est impossible.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"0.35\", \"b\": \"1.2\", \"c\": \"0.85\", \"d\": \"0.2\"}}","_debug_options_count":4},{"id":4743,"question":"La loi de probabilité qui modélise le temps d'attente entre deux événements aléatoires est :","option_a":"Loi binomiale","option_b":"Loi normale","option_c":"Loi exponentielle","option_d":"Loi uniforme","option_e":"","option_f":"","bonne_reponse":"c","explication":"La loi exponentielle modélise le temps d'attente entre deux événements aléatoires dans un processus de Poisson.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"Loi binomiale\", \"b\": \"Loi normale\", \"c\": \"Loi exponentielle\", \"d\"","_debug_options_count":4},{"id":4744,"question":"Si P(A) = 0.3 et P(B|A) = 0.6, alors P(A ∩ B) = ?","option_a":"0.18","option_b":"0.9","option_c":"0.36","option_d":"0.08","option_e":"","option_f":"","bonne_reponse":"a","explication":"P(A ∩ B) = P(B|A) × P(A) = 0.6 × 0.3 = 0.18.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"0.18\", \"b\": \"0.9\", \"c\": \"0.36\", \"d\": \"0.08\"}}","_debug_options_count":4},{"id":4745,"question":"La probabilité d'un événement certain est toujours égale à 1.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Vrai. Par définition, un événement certain a une probabilité de 1.","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}]