Quiz — سلسلة تمارين في الاحتمالات للسنة 2 ثانوي من اعداد الاستاذ مرنيز وليد.pdf

Question 1 sur 10 20:00

[{"id":3184,"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\/2","option_c":"1\/3","option_d":"2\/3","option_e":"","option_f":"","bonne_reponse":"b","explication":"Il y 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\": \"b\", \"options\": {\"a\": \"1\/6\", \"b\": \"1\/2\", \"c\": \"1\/3\", \"d\": \"2\/3\"}}","_debug_options_count":4},{"id":3185,"question":"Si A et B sont deux événements incompatibles, alors P(A ∩ B) = 0.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Par définition, deux événements incompatibles ne peuvent pas se produire simultanément, donc P(A ∩ B) = 0.","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":3186,"question":"Dans une urne contenant 4 boules rouges et 6 boules bleues, quelle est la probabilité de tirer une boule rouge ?","option_a":"2\/5","option_b":"3\/5","option_c":"4\/10","option_d":"6\/10","option_e":"","option_f":"","bonne_reponse":"a","explication":"Il y a 4 boules rouges sur un total de 10 boules. La probabilité est donc 4\/10 = 2\/5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"2\/5\", \"b\": \"3\/5\", \"c\": \"4\/10\", \"d\": \"6\/10\"}}","_debug_options_count":4},{"id":3187,"question":"La loi binomiale s'applique uniquement à des expériences répétées un nombre infini de fois.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La loi binomiale s'applique à des expériences répétées un nombre fini de fois, avec une probabilité de succès constante.","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":3188,"question":"Quelle est la probabilité d'obtenir exactement 2 fois le chiffre 6 en lançant un dé 5 fois ?","option_a":"5\/32","option_b":"10\/32","option_c":"1\/6","option_d":"5\/6","option_e":"","option_f":"","bonne_reponse":"b","explication":"C'est un problème de loi binomiale avec n=5, k=2 et p=1\/6. La probabilité est C(5,2) * (1\/6)^2 * (5\/6)^3 = 10 * (1\/36) * (125\/216) ≈ 10\/32.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"5\/32\", \"b\": \"10\/32\", \"c\": \"1\/6\", \"d\": \"5\/6\"}}","_debug_options_count":4},{"id":3189,"question":"Si P(A) = 0.4 et P(B) = 0.5, alors P(A ∪ B) = 0.9.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"P(A ∪ B) = P(A) + P(B) - P(A ∩ B). Sans connaître P(A ∩ B), on ne peut pas affirmer que P(A ∪ B) = 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\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":3190,"question":"Dans une classe de 30 élèves, 12 sont des filles. Quelle est la probabilité de choisir un garçon au hasard ?","option_a":"12\/30","option_b":"18\/30","option_c":"1\/2","option_d":"3\/5","option_e":"","option_f":"","bonne_reponse":"b","explication":"Il y a 18 garçons sur 30 élèves. La probabilité est donc 18\/30 = 3\/5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"12\/30\", \"b\": \"18\/30\", \"c\": \"1\/2\", \"d\": \"3\/5\"}}","_debug_options_count":4},{"id":3191,"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":3192,"question":"Quelle est la probabilité d'obtenir au moins un 6 en lançant un dé 3 fois ?","option_a":"1\/2","option_b":"91\/216","option_c":"1\/6","option_d":"125\/216","option_e":"","option_f":"","bonne_reponse":"b","explication":"La probabilité d'obtenir au moins un 6 est 1 - P(aucun 6) = 1 - (5\/6)^3 = 1 - 125\/216 = 91\/216.","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\": \"91\/216\", \"c\": \"1\/6\", \"d\": \"125\/216\"}}","_debug_options_count":4},{"id":3193,"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":"C'est la définition de l'indépendance entre deux événements. P(A ∩ B) = P(A) * P(B) si A et B sont indépendants.","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}]