Quiz — مجلة الرائد في حلول تمارين الإحتمالات (2017-2018) للأستاذ بالعبيدي محمد العربي.pdf

Question 1 sur 10 20:00

[{"id":42965,"question":"Quelle est la probabilité d'obtenir un nombre pair en lançant un dé équilibré à 6 faces ?","option_a":"1\/2","option_b":"1\/3","option_c":"1\/6","option_d":"2\/3","option_e":"","option_f":"","bonne_reponse":"a","explication":"Un dé équilibré a 6 faces (1, 2, 3, 4, 5, 6). Les nombres pairs sont 2, 4, 6, soit 3 cas favorables sur 6 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\": \"a\", \"options\": {\"a\": \"1\/2\", \"b\": \"1\/3\", \"c\": \"1\/6\", \"d\": \"2\/3\"}}","_debug_options_count":4},{"id":42966,"question":"Deux événements A et B sont indépendants si 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. Si cette égalité est vérifiée, alors 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},{"id":42967,"question":"Dans une urne contenant 4 boules rouges et 6 boules bleues, quelle est la probabilité de tirer une boule bleue ?","option_a":"3\/5","option_b":"2\/5","option_c":"6\/10","option_d":"4\/10","option_e":"","option_f":"","bonne_reponse":"c","explication":"Il y a 6 boules bleues sur un total de 10 boules (4 rouges + 6 bleues). La probabilité est donc 6\/10 = 3\/5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"3\/5\", \"b\": \"2\/5\", \"c\": \"6\/10\", \"d\": \"4\/10\"}}","_debug_options_count":4},{"id":42968,"question":"La probabilité d'un événement impossible est égale à :","option_a":"0","option_b":"1","option_c":"0.5","option_d":"1\/2","option_e":"","option_f":"","bonne_reponse":"a","explication":"Un événement impossible ne peut pas se produire, donc sa probabilité est toujours 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\": \"0\", \"b\": \"1\", \"c\": \"0.5\", \"d\": \"1\/2\"}}","_debug_options_count":4},{"id":42969,"question":"Si P(A) = 0.3 et P(B) = 0.4, et que A et B sont incompatibles, alors P(A ∪ B) = 0.7.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour deux événements incompatibles, P(A ∪ B) = P(A) + P(B) = 0.3 + 0.4 = 0.7. L'affirmation est donc vraie.","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":42970,"question":"Quelle formule permet de calculer la probabilité conditionnelle P(A|B) ?","option_a":"P(A|B) = P(A ∩ B) \/ P(B)","option_b":"P(A|B) = P(A) + P(B)","option_c":"P(A|B) = P(A) × P(B)","option_d":"P(A|B) = P(A) \/ P(B)","option_e":"","option_f":"","bonne_reponse":"a","explication":"La probabilité conditionnelle P(A|B) se calcule en divisant la probabilité de l'intersection P(A ∩ B) par la probabilité de 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\": \"P(A|B) = P(A ∩ B) \/ P(B)\", \"b\": \"P(A|B) = P(A) + P(B)\", \"c\": \"P","_debug_options_count":4},{"id":42971,"question":"Dans un jeu de 52 cartes, quelle est la probabilité de tirer un as ?","option_a":"1\/13","option_b":"1\/4","option_c":"4\/52","option_d":"1\/52","option_e":"","option_f":"","bonne_reponse":"a","explication":"Il y a 4 as dans un jeu de 52 cartes. La probabilité est donc 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\": \"4\/52\", \"d\": \"1\/52\"}}","_debug_options_count":4},{"id":42972,"question":"Si deux événements A et B sont tels que P(A) = 0.6 et P(B) = 0.5, alors P(A ∪ B) ≤ 1.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La probabilité d'une union de deux événements est toujours ≤ 1, car une probabilité ne peut pas dépasser 1. L'affirmation est donc vraie.","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":42973,"question":"Quelle est la probabilité d'obtenir deux fois pile en lançant deux fois 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 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":42974,"question":"La probabilité d'un événement certain est égale à :","option_a":"0","option_b":"1","option_c":"0.5","option_d":"1\/2","option_e":"","option_f":"","bonne_reponse":"b","explication":"Un événement certain se produit à coup sûr, donc sa probabilité est toujours 1.","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\", \"b\": \"1\", \"c\": \"0.5\", \"d\": \"1\/2\"}}","_debug_options_count":4}]