Quiz — تمرين-في-الاحتمالات.pdf

Question 1 sur 10 20:00

[{"id":15009,"question":"Quelle est la probabilité d'obtenir exactement 3 fois pile en 5 lancers d'une pièce équilibrée ?","option_a":"1\/32","option_b":"5\/16","option_c":"10\/32","option_d":"15\/32","option_e":"","option_f":"","bonne_reponse":"c","explication":"La probabilité suit une loi binomiale B(5, 0.5). P(X=3) = C(5,3) * (0.5)^5 = 10\/32.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"1\/32\", \"b\": \"5\/16\", \"c\": \"10\/32\", \"d\": \"15\/32\"}}","_debug_options_count":4},{"id":15010,"question":"Si X suit une loi normale N(0,1), alors P(X ≤ 1) est égale à :","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"P(X ≤ 1) ≈ 0.8413 (valeur lue dans la table de la loi normale centrée réduite).","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":15011,"question":"L'espérance d'une variable aléatoire suivant une loi uniforme sur [a,b] est égale à :","option_a":"(a+b)\/2","option_b":"a+b","option_c":"b-a","option_d":"(a-b)\/2","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour une loi uniforme U(a,b), E(X) = (a+b)\/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\": \"(a+b)\/2\", \"b\": \"a+b\", \"c\": \"b-a\", \"d\": \"(a-b)\/2\"}}","_debug_options_count":4},{"id":15012,"question":"Deux événements A et B sont indépendants si et seulement si :","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'indépendance se définit par 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":15013,"question":"Quelle est la variance d'une variable aléatoire suivant une loi de Bernoulli de paramètre p ?","option_a":"p","option_b":"1-p","option_c":"p(1-p)","option_d":"p²","option_e":"","option_f":"","bonne_reponse":"c","explication":"Pour une loi de Bernoulli B(p), Var(X) = p(1-p).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"p\", \"b\": \"1-p\", \"c\": \"p(1-p)\", \"d\": \"p²\"}}","_debug_options_count":4},{"id":15014,"question":"Si X ~ N(μ, σ²), alors P(μ - σ ≤ X ≤ μ + σ) est environ égal à :","option_a":"68%","option_b":"95%","option_c":"99%","option_d":"50%","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour une loi normale, environ 68% des valeurs sont dans l'intervalle [μ-σ, μ+σ].","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"68%\", \"b\": \"95%\", \"c\": \"99%\", \"d\": \"50%\"}}","_debug_options_count":4},{"id":15015,"question":"Un dé équilibré est lancé 10 fois. Quelle est la probabilité d'obtenir au moins un 6 ?","option_a":"1 - (5\/6)^10","option_b":"10*(1\/6)","option_c":"(1\/6)^10","option_d":"5\/6","option_e":"","option_f":"","bonne_reponse":"a","explication":"P(au moins un 6) = 1 - P(aucun 6) = 1 - (5\/6)^10.","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 - (5\/6)^10\", \"b\": \"10*(1\/6)\", \"c\": \"(1\/6)^10\", \"d\": \"5\/6\"}}","_debug_options_count":4},{"id":15016,"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":15017,"question":"Quelle est l'espérance d'une variable aléatoire X suivant une loi exponentielle de paramètre λ ?","option_a":"λ","option_b":"1\/λ","option_c":"λ²","option_d":"1\/λ²","option_e":"","option_f":"","bonne_reponse":"b","explication":"Pour une loi exponentielle Exp(λ), E(X) = 1\/λ.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"λ\", \"b\": \"1\/λ\", \"c\": \"λ²\", \"d\": \"1\/λ²\"}}","_debug_options_count":4},{"id":15018,"question":"Deux événements A et B sont incompatibles si et seulement si P(A∩B) = 0.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Des événements incompatibles ont une intersection vide, 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}]