Quiz — ملخص احتمالات (( تيلولت )) .pdf

Question 1 sur 10 20:00

[{"id":102723,"question":"Quelle est la formule de la probabilité d'un événement A ?","option_a":"P(A) = nombre de cas favorables \/ nombre de cas possibles","option_b":"P(A) = nombre de cas possibles \/ nombre de cas favorables","option_c":"P(A) = 1 - P(A)","option_d":"P(A) = P(A) + P(B)","option_e":"","option_f":"","bonne_reponse":"a","explication":"La probabilité d'un événement A est définie comme le rapport entre le nombre de cas favorables et le nombre total de cas possibles.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"P(A) = nombre de cas favorables \/ nombre de cas possibles\", \"b\": ","_debug_options_count":4},{"id":102724,"question":"Deux événements A et B sont incompatibles si :","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Deux événements sont incompatibles s'ils ne peuvent pas se produire simultanément, c'est-à-dire que 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},{"id":102725,"question":"Quelle est la valeur de C(5,2) ?","option_a":"10","option_b":"15","option_c":"20","option_d":"5","option_e":"","option_f":"","bonne_reponse":"a","explication":"C(5,2) = 5! \/ (2! * 3!) = 10. C'est le nombre de façons de choisir 2 éléments parmi 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"10\", \"b\": \"15\", \"c\": \"20\", \"d\": \"5\"}}","_debug_options_count":4},{"id":102726,"question":"Dans une loi binomiale de paramètres n et p, l'espérance est égale à :","option_a":"n * p","option_b":"n + p","option_c":"p \/ n","option_d":"n² * p","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'espérance d'une loi binomiale B(n,p) est E(X) = n * p, où n est le nombre d'essais et p la probabilité de succès.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"n * p\", \"b\": \"n + p\", \"c\": \"p \/ n\", \"d\": \"n² * p\"}}","_debug_options_count":4},{"id":102727,"question":"La probabilité d'un événement certain est toujours égale à 0.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La probabilité d'un événement certain est égale à 1, car il se produit à coup sûr.","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":102728,"question":"Quelle est la probabilité d'obtenir un 6 en lançant un dé équilibré ?","option_a":"1\/6","option_b":"1\/3","option_c":"1\/2","option_d":"2\/3","option_e":"","option_f":"","bonne_reponse":"a","explication":"Un dé équilibré a 6 faces, chacune avec une probabilité de 1\/6 d'apparaître.","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\/3\", \"c\": \"1\/2\", \"d\": \"2\/3\"}}","_debug_options_count":4},{"id":102729,"question":"Deux événements A et B sont indépendants si :","option_a":"P(A ∩ B) = P(A) * P(B)","option_b":"P(A ∩ B) = P(A) + P(B)","option_c":"P(A ∩ B) = 0","option_d":"P(A ∩ B) = 1","option_e":"","option_f":"","bonne_reponse":"a","explication":"Deux événements sont indépendants si la réalisation de l'un n'influence pas la probabilité de l'autre, soit 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\": \"P(A ∩ B) = P(A) * P(B)\", \"b\": \"P(A ∩ B) = P(A) + P(B)\", \"c\": ","_debug_options_count":4},{"id":102730,"question":"Dans une loi uniforme sur {1, 2, 3, 4, 5, 6}, la probabilité d'obtenir un nombre pair est :","option_a":"1\/2","option_b":"1\/3","option_c":"2\/3","option_d":"1\/6","option_e":"","option_f":"","bonne_reponse":"a","explication":"Il y a 3 nombres pairs (2, 4, 6) sur 6 possibles, donc la probabilité est 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\": \"a\", \"options\": {\"a\": \"1\/2\", \"b\": \"1\/3\", \"c\": \"2\/3\", \"d\": \"1\/6\"}}","_debug_options_count":4},{"id":102731,"question":"La variance d'une loi binomiale B(n,p) est égale à :","option_a":"n * p * (1 - p)","option_b":"n² * p","option_c":"n * p","option_d":"p * (1 - p)","option_e":"","option_f":"","bonne_reponse":"a","explication":"La variance d'une loi binomiale B(n,p) est V(X) = n * p * (1 - 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\": \"n * p * (1 - p)\", \"b\": \"n² * p\", \"c\": \"n * p\", \"d\": \"p * (1 - p)","_debug_options_count":4},{"id":102732,"question":"Si P(A) = 0.4 et P(B) = 0.5, et que A et B sont indépendants, alors P(A ∩ B) = :","option_a":"0.2","option_b":"0.9","option_c":"0.1","option_d":"0.45","option_e":"","option_f":"","bonne_reponse":"a","explication":"Puisque A et B sont indépendants, P(A ∩ B) = P(A) * P(B) = 0.4 * 0.5 = 0.2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"0.2\", \"b\": \"0.9\", \"c\": \"0.1\", \"d\": \"0.45\"}}","_debug_options_count":4}]