Quiz — Lycée Pilote Sfax - Probabilité 6.pdf

Question 1 sur 10 20:00

[{"id":47973,"question":"Quelle est la probabilité d'obtenir exactement 3 succès dans une expérience suivant une loi binomiale de paramètres n=5 et p=0.4 ?","option_a":"0.2304","option_b":"0.3456","option_c":"0.4096","option_d":"0.1536","option_e":"","option_f":"","bonne_reponse":"a","explication":"La probabilité est donnée par P(X=3) = C(5,3) * (0.4)^3 * (0.6)^2 = 10 * 0.064 * 0.36 = 0.2304.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"0.2304\", \"b\": \"0.3456\", \"c\": \"0.4096\", \"d\": \"0.1536\"}}","_debug_options_count":4},{"id":47974,"question":"L'espérance d'une variable aléatoire suivant une loi binomiale est toujours égale à n*p.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"C'est une propriété fondamentale de la loi binomiale : E(X) = n*p.","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":47975,"question":"Quelle est la variance d'une variable aléatoire suivant une loi binomiale de paramètres n=10 et p=0.3 ?","option_a":"2.1","option_b":"3.0","option_c":"2.7","option_d":"1.8","option_e":"","option_f":"","bonne_reponse":"a","explication":"La variance est donnée par V(X) = n*p*(1-p) = 10*0.3*0.7 = 2.1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"2.1\", \"b\": \"3.0\", \"c\": \"2.7\", \"d\": \"1.8\"}}","_debug_options_count":4},{"id":47976,"question":"Si X suit une loi binomiale B(8, 0.5), quelle est la probabilité que X soit supérieure ou égale à 5 ?","option_a":"0.3633","option_b":"0.6367","option_c":"0.1445","option_d":"0.8555","option_e":"","option_f":"","bonne_reponse":"b","explication":"P(X≥5) = 1 - P(X≤4) = 1 - 0.6367 = 0.3633 (valeur arrondie).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"0.3633\", \"b\": \"0.6367\", \"c\": \"0.1445\", \"d\": \"0.8555\"}}","_debug_options_count":4},{"id":47977,"question":"La fonction de répartition d'une variable aléatoire discrète est toujours continue.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La fonction de répartition d'une variable discrète est discontinue aux points de discontinuité de la variable.","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":47978,"question":"Quelle est la probabilité d'obtenir au moins un succès dans une série de 4 épreuves indépendantes avec p=0.2 ?","option_a":"0.5904","option_b":"0.4096","option_c":"0.8000","option_d":"0.2000","option_e":"","option_f":"","bonne_reponse":"a","explication":"P(X≥1) = 1 - P(X=0) = 1 - (0.8)^4 = 1 - 0.4096 = 0.5904.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"0.5904\", \"b\": \"0.4096\", \"c\": \"0.8000\", \"d\": \"0.2000\"}}","_debug_options_count":4},{"id":47979,"question":"Si X suit une loi binomiale B(n,p), alors X peut prendre des valeurs négatives.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Une variable aléatoire suivant une loi binomiale prend des valeurs entières comprises entre 0 et n.","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":47980,"question":"Quelle est l'espérance d'une variable aléatoire X suivant une loi binomiale B(7, 0.6) ?","option_a":"4.2","option_b":"2.8","option_c":"3.5","option_d":"5.0","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'espérance est donnée par E(X) = n*p = 7*0.6 = 4.2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"4.2\", \"b\": \"2.8\", \"c\": \"3.5\", \"d\": \"5.0\"}}","_debug_options_count":4},{"id":47981,"question":"La variance d'une variable aléatoire suivant une loi binomiale est toujours supérieure à son espérance.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La variance est n*p*(1-p), qui peut être inférieure à n*p si p\u003E0.5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":47982,"question":"Quelle est la probabilité d'obtenir exactement 2 succès dans une expérience suivant une loi binomiale de paramètres n=6 et p=0.3 ?","option_a":"0.3240","option_b":"0.2554","option_c":"0.1852","option_d":"0.4116","option_e":"","option_f":"","bonne_reponse":"b","explication":"La probabilité est donnée par P(X=2) = C(6,2) * (0.3)^2 * (0.7)^4 = 15 * 0.09 * 0.2401 ≈ 0.2554.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"0.3240\", \"b\": \"0.2554\", \"c\": \"0.1852\", \"d\": \"0.4116\"}}","_debug_options_count":4}]