Quiz — cours-probabilités.pdf

Question 1 sur 10 20:00

[{"id":146878,"question":"Quelle est la probabilité d’obtenir un 6 en lançant un dé équilibré ?","option_a":"1\/6","option_b":"1\/2","option_c":"1\/3","option_d":"1\/4","option_e":"","option_f":"","bonne_reponse":"a","explication":"Un dé équilibré a 6 faces numérotées de 1 à 6. La probabilité d’obtenir un 6 est donc 1\/6.","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\/6\", \"b\": \"1\/2\", \"c\": \"1\/3\", \"d\": \"1\/4\"}}","_debug_options_count":4},{"id":146879,"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 que 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":146880,"question":"Dans une loi binomiale de paramètres n=5 et p=0.3, quelle est la probabilité d’avoir exactement 2 succès ?","option_a":"C(5,2) × (0.3)² × (0.7)³","option_b":"C(5,2) × (0.3)³ × (0.7)²","option_c":"(0.3)²","option_d":"(0.3)⁵","option_e":"","option_f":"","bonne_reponse":"a","explication":"La formule de la loi binomiale est P(X=k) = C(n,k) × p^k × (1-p)^(n-k). Ici, k=2, n=5, p=0.3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"C(5,2) × (0.3)² × (0.7)³\", \"b\": \"C(5,2) × (0.3)³ × (0.7)²","_debug_options_count":4},{"id":146881,"question":"Si P(A) = 0.4 et P(B) = 0.5, et que A et B sont indépendants, 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":"a","explication":"Pour des événements indépendants, P(A ∩ B) = P(A) × P(B) = 0.4 × 0.5 = 0.2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"0.2\", \"b\": \"0.9\", \"c\": \"0.1\", \"d\": \"0.5\"}}","_debug_options_count":4},{"id":146882,"question":"La probabilité d’un événement impossible est toujours égale à 1.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La probabilité d’un événement impossible est égale à 0, tandis que celle d’un événement certain est égale à 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\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":146883,"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":"4\/52","option_e":"","option_f":"","bonne_reponse":"a","explication":"Un jeu de 52 cartes contient 4 as. La probabilité de tirer un as 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\": \"1\/52\", \"d\": \"4\/52\"}}","_debug_options_count":4},{"id":146884,"question":"Dans une classe de 30 élèves, 12 sont des filles. Quelle est la probabilité de choisir une fille au hasard ?","option_a":"12\/30","option_b":"18\/30","option_c":"1\/30","option_d":"30\/12","option_e":"","option_f":"","bonne_reponse":"a","explication":"Il y a 12 filles sur 30 élèves. La probabilité de choisir une fille est donc 12\/30 = 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\": \"12\/30\", \"b\": \"18\/30\", \"c\": \"1\/30\", \"d\": \"30\/12\"}}","_debug_options_count":4},{"id":146885,"question":"Si P(A) = 0.6 et P(B) = 0.3, et que A et B sont incompatibles, alors P(A ∪ B) = ?","option_a":"0.9","option_b":"0.18","option_c":"0.3","option_d":"0.6","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour des événements incompatibles, P(A ∪ B) = P(A) + P(B) = 0.6 + 0.3 = 0.9.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"0.9\", \"b\": \"0.18\", \"c\": \"0.3\", \"d\": \"0.6\"}}","_debug_options_count":4},{"id":146886,"question":"La loi uniforme discrète s’applique lorsque :","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La loi uniforme discrète s’applique lorsque toutes les issues possibles ont la même probabilité, comme dans le lancer d’un dé équilibré.","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":146887,"question":"Quelle est la probabilité de ne pas obtenir un 1 en lançant un dé à 6 faces ?","option_a":"5\/6","option_b":"1\/6","option_c":"1\/2","option_d":"2\/3","option_e":"","option_f":"","bonne_reponse":"a","explication":"La probabilité d’obtenir un 1 est 1\/6. Donc, la probabilité de ne pas obtenir un 1 est 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\": \"a\", \"options\": {\"a\": \"5\/6\", \"b\": \"1\/6\", \"c\": \"1\/2\", \"d\": \"2\/3\"}}","_debug_options_count":4}]