Quiz — درس احتمالات ثالثة علوم.pdf

Question 1 sur 10 20:00

[{"id":68626,"question":"Quelle est la probabilité d'obtenir un nombre pair en lançant un dé équilibré à 6 faces ?","option_a":"1\/6","option_b":"1\/3","option_c":"1\/2","option_d":"2\/3","option_e":"","option_f":"","bonne_reponse":"c","explication":"Il y a 3 nombres pairs (2, 4, 6) sur 6 faces possibles. La probabilité est donc 3\/6 = 1\/2.","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\/6\", \"b\": \"1\/3\", \"c\": \"1\/2\", \"d\": \"2\/3\"}}","_debug_options_count":4},{"id":68627,"question":"Si P(A) = 0.4 et P(B) = 0.5, et que A et B sont incompatibles, quelle est P(A ∪ B) ?","option_a":"0.2","option_b":"0.4","option_c":"0.5","option_d":"0.9","option_e":"","option_f":"","bonne_reponse":"d","explication":"Pour des événements incompatibles, P(A ∪ B) = P(A) + P(B) = 0.4 + 0.5 = 0.9.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"d\", \"options\": {\"a\": \"0.2\", \"b\": \"0.4\", \"c\": \"0.5\", \"d\": \"0.9\"}}","_debug_options_count":4},{"id":68628,"question":"Vrai ou Faux ? La loi binomiale s'applique uniquement à des expériences à deux issues possibles.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La loi binomiale s'applique à une série d'expériences indépendantes à deux issues (succès\/échec), comme le lancer de pièce.","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":68629,"question":"Quelle est l'espérance d'une variable aléatoire X suivant une loi de Bernoulli de paramètre p = 0.3 ?","option_a":"0.3","option_b":"0.7","option_c":"0.1","option_d":"0.5","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour une loi de Bernoulli, E(X) = 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\": \"0.3\", \"b\": \"0.7\", \"c\": \"0.1\", \"d\": \"0.5\"}}","_debug_options_count":4},{"id":68630,"question":"Si X suit une loi normale N(μ=5, σ=2), quelle est la probabilité que X soit inférieure à 5 ?","option_a":"0.25","option_b":"0.5","option_c":"0.75","option_d":"0.95","option_e":"","option_f":"","bonne_reponse":"b","explication":"Dans une loi normale, la probabilité que X soit inférieure à la moyenne μ est de 0.5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"0.25\", \"b\": \"0.5\", \"c\": \"0.75\", \"d\": \"0.95\"}}","_debug_options_count":4},{"id":68631,"question":"Vrai ou Faux ? La variance d'une variable aléatoire mesure la dispersion des valeurs autour de l'espérance.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La variance mesure bien la dispersion des valeurs autour de l'espérance mathématique.","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":68632,"question":"Quelle est la probabilité d'obtenir exactement 2 succès en 5 essais indépendants, si la probabilité de succès est de 0.4 ?","option_a":"0.2304","option_b":"0.3456","option_c":"0.1664","option_d":"0.07776","option_e":"","option_f":"","bonne_reponse":"b","explication":"C'est une application de la loi binomiale : C(5,2) * (0.4)^2 * (0.6)^3 = 10 * 0.16 * 0.216 = 0.3456.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"0.2304\", \"b\": \"0.3456\", \"c\": \"0.1664\", \"d\": \"0.07776\"}}","_debug_options_count":4},{"id":68633,"question":"Si P(A|B) = 0.6 et P(B) = 0.5, quelle est P(A ∩ B) ?","option_a":"0.1","option_b":"0.3","option_c":"0.6","option_d":"0.8","option_e":"","option_f":"","bonne_reponse":"b","explication":"P(A ∩ B) = P(A|B) * P(B) = 0.6 * 0.5 = 0.3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"0.1\", \"b\": \"0.3\", \"c\": \"0.6\", \"d\": \"0.8\"}}","_debug_options_count":4},{"id":68634,"question":"Vrai ou Faux ? L'écart-type est toujours positif ou nul.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'écart-type, comme la variance, est toujours positif ou nul car il s'agit d'une mesure de dispersion.","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":68635,"question":"Quelle est la probabilité que X soit supérieur à 7 dans une loi normale N(μ=5, σ=1) ?","option_a":"0.0228","option_b":"0.1587","option_c":"0.5","option_d":"0.9772","option_e":"","option_f":"","bonne_reponse":"a","explication":"En utilisant la table de la loi normale, P(X \u003E 7) = 1 - P(X ≤ 7) ≈ 1 - 0.9772 = 0.0228.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"0.0228\", \"b\": \"0.1587\", \"c\": \"0.5\", \"d\": \"0.9772\"}}","_debug_options_count":4}]