Maîtrisez les probabilités pour le Bac : Quiz interactif

Question 1 sur 10 10:00

[{"id":47541,"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},{"id":47542,"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},{"id":47543,"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},{"id":47544,"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},{"id":47545,"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},{"id":47546,"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},{"id":47547,"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},{"id":47548,"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},{"id":47549,"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},{"id":47550,"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}]