Quiz — 30 تمرين في الاحتمالات -2020.pdf

Question 1 sur 10 20:00

[{"id":5036,"question":"Quelle est la formule de la probabilité conditionnelle P(A|B) ?","option_a":"P(A) × P(B)","option_b":"P(A∩B) \/ P(B)","option_c":"P(A) + P(B)","option_d":"P(A∪B)","option_e":"","option_f":"","bonne_reponse":"b","explication":"La probabilité conditionnelle P(A|B) se calcule en divisant la probabilité de l'intersection de A et 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\": \"b\", \"options\": {\"a\": \"P(A) × P(B)\", \"b\": \"P(A∩B) \/ P(B)\", \"c\": \"P(A) + P(B)\", \"d\": \"","_debug_options_count":4},{"id":5037,"question":"Dans une loi binomiale de paramètres n=10 et p=0,3, quelle est l'espérance ?","option_a":"3","option_b":"10","option_c":"7","option_d":"0,3","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'espérance d'une loi binomiale B(n,p) est égale à n × p, soit 10 × 0,3 = 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\": \"3\", \"b\": \"10\", \"c\": \"7\", \"d\": \"0,3\"}}","_debug_options_count":4},{"id":5038,"question":"Vrai ou Faux ? La variance d'une loi uniforme sur [a,b] est (b-a)²\/12.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La variance d'une loi uniforme sur [a,b] est bien (b-a)²\/12.","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":5039,"question":"Quelle loi de probabilité modélise le nombre de succès dans une série d'essais indépendants identiques ?","option_a":"Loi normale","option_b":"Loi binomiale","option_c":"Loi exponentielle","option_d":"Loi uniforme","option_e":"","option_f":"","bonne_reponse":"b","explication":"La loi binomiale modélise le nombre de succès dans une série d'essais indépendants et identiques.","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 normale\", \"b\": \"Loi binomiale\", \"c\": \"Loi exponentielle\", \"d\"","_debug_options_count":4},{"id":5040,"question":"Vrai ou Faux ? La probabilité de l'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":"Par définition, la probabilité de l'événement certain est toujours égale à 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},{"id":5041,"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\/12","option_e":"","option_f":"","bonne_reponse":"a","explication":"Un dé équilibré a 6 faces, donc la probabilité d'obtenir un 6 est 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\/12\"}}","_debug_options_count":4},{"id":5042,"question":"Dans une loi normale centrée réduite, quelle est la probabilité P(-1 ≤ X ≤ 1) ?","option_a":"0,68","option_b":"0,95","option_c":"0,99","option_d":"0,34","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour une loi normale centrée réduite, P(-1 ≤ X ≤ 1) ≈ 0,68 (règle des 68-95-99,7).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"0,68\", \"b\": \"0,95\", \"c\": \"0,99\", \"d\": \"0,34\"}}","_debug_options_count":4},{"id":5043,"question":"Vrai ou Faux ? La probabilité de l'intersection de deux événements indépendants est le produit de leurs probabilités.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Si deux événements sont indépendants, alors 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":5044,"question":"Quelle est la probabilité de ne pas obtenir un 5 en lançant un dé équilibré ?","option_a":"5\/6","option_b":"1\/6","option_c":"2\/3","option_d":"1\/2","option_e":"","option_f":"","bonne_reponse":"a","explication":"La probabilité de ne pas obtenir un 5 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\": \"2\/3\", \"d\": \"1\/2\"}}","_debug_options_count":4},{"id":5045,"question":"Vrai ou Faux ? La loi exponentielle modélise des phénomènes sans mémoire.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La loi exponentielle est souvent utilisée pour modéliser des phénomènes sans mémoire, comme la durée de vie d'un composant.","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}]