Quiz — 65d6251c637d7_énoncé_Magazine 15 - Probabilité conditionnelle (1).pdf

Question 1 sur 10 20:00

[{"id":16509,"question":"Soit deux événements A et B tels que P(A) = 0,4, P(B) = 0,5 et P(A ∩ B) = 0,2. Quelle est la valeur de P(A|B) ?","option_a":"0,2","option_b":"0,4","option_c":"0,5","option_d":"0,8","option_e":"","option_f":"","bonne_reponse":"b","explication":"P(A|B) = P(A ∩ B) \/ P(B) = 0,2 \/ 0,5 = 0,4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"0,2\", \"b\": \"0,4\", \"c\": \"0,5\", \"d\": \"0,8\"}}","_debug_options_count":4},{"id":16510,"question":"Si P(A|B) = 0,7 et P(B) = 0,3, alors P(A ∩ B) = ?","option_a":"0,21","option_b":"0,3","option_c":"0,7","option_d":"0,1","option_e":"","option_f":"","bonne_reponse":"a","explication":"P(A ∩ B) = P(A|B) * P(B) = 0,7 * 0,3 = 0,21.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"0,21\", \"b\": \"0,3\", \"c\": \"0,7\", \"d\": \"0,1\"}}","_debug_options_count":4},{"id":16511,"question":"Les probabilités conditionnelles ne peuvent être calculées que pour des événements indépendants.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Les probabilités conditionnelles s'appliquent aux événements dépendants ou indépendants, mais leur calcul est particulièrement utile pour les événements dépendants.","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":16512,"question":"Dans un jeu de cartes, on tire une carte au hasard. Soit A l'événement 'tirer un roi' et B l'événement 'tirer une carte rouge'. Quelle est P(A|B) ?","option_a":"1\/13","option_b":"2\/13","option_c":"1\/26","option_d":"4\/52","option_e":"","option_f":"","bonne_reponse":"b","explication":"Il y a 2 rois rouges sur 26 cartes rouges, donc P(A|B) = 2\/26 = 1\/13.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"1\/13\", \"b\": \"2\/13\", \"c\": \"1\/26\", \"d\": \"4\/52\"}}","_debug_options_count":4},{"id":16513,"question":"Si P(A|B) = P(A), alors les événements A et B sont indépendants.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Si P(A|B) = P(A), cela signifie que la réalisation de B n'influence pas celle de A, donc A et B sont indépendants.","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":16514,"question":"Un test médical a une probabilité de 0,95 de détecter une maladie chez une personne malade. Quelle est la probabilité que le test soit positif sachant que la personne est malade ?","option_a":"0,05","option_b":"0,95","option_c":"0,5","option_d":"1","option_e":"","option_f":"","bonne_reponse":"b","explication":"La probabilité que le test soit positif sachant que la personne est malade est la sensibilité du test, soit 0,95.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"0,05\", \"b\": \"0,95\", \"c\": \"0,5\", \"d\": \"1\"}}","_debug_options_count":4},{"id":16515,"question":"Soit A et B deux événements tels que P(A) = 0,6, P(B) = 0,4 et P(A ∩ B) = 0,2. Les événements A et B sont-ils indépendants ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Pour que A et B soient indépendants, il faut P(A ∩ B) = P(A) * P(B) = 0,24. Or P(A ∩ B) = 0,2 ≠ 0,24, donc ils ne sont pas indépendants.","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":16516,"question":"Dans une classe de 30 élèves, 18 sont des filles et 12 sont des garçons. Parmi les filles, 6 portent des lunettes. Quelle est la probabilité qu'un élève choisi au hasard porte des lunettes sachant que c'est une fille ?","option_a":"0,2","option_b":"0,33","option_c":"0,5","option_d":"0,6","option_e":"","option_f":"","bonne_reponse":"c","explication":"Parmi les 18 filles, 6 portent des lunettes, donc P(lunettes|fille) = 6\/18 = 1\/3 ≈ 0,33.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"0,2\", \"b\": \"0,33\", \"c\": \"0,5\", \"d\": \"0,6\"}}","_debug_options_count":4},{"id":16517,"question":"La probabilité conditionnelle P(A|B) est toujours inférieure ou égale à P(A).","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"P(A|B) peut être supérieure à P(A) si B favorise A (par exemple, si B est un sous-ensemble de A).","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":16518,"question":"Soit A et B deux événements tels que P(A) = 0,5, P(B) = 0,5 et P(A ∩ B) = 0,3. Quelle est la valeur de P(B|A) ?","option_a":"0,3","option_b":"0,5","option_c":"0,6","option_d":"0,7","option_e":"","option_f":"","bonne_reponse":"c","explication":"P(B|A) = P(A ∩ B) \/ P(A) = 0,3 \/ 0,5 = 0,6.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"0,3\", \"b\": \"0,5\", \"c\": \"0,6\", \"d\": \"0,7\"}}","_debug_options_count":4}]