Quiz — 64355f1b58e97_énoncé_Probabilité classique.pdf

Question 1 sur 5 10:00

[{"id":2763,"question":"Dans une urne contenant 3 boules rouges et 2 boules bleues, quelle est la probabilité de tirer une boule rouge ?","option_a":"0,4","option_b":"0,6","option_c":"0,5","option_d":"0,3","option_e":"","option_f":"","bonne_reponse":"b","explication":"La probabilité est calculée en divisant le nombre de cas favorables (3 boules rouges) par le nombre total de cas (5 boules). P(rouge) = 3\/5 = 0,6.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"0,4\", \"b\": \"0,6\", \"c\": \"0,5\", \"d\": \"0,3\"}}","_debug_options_count":4},{"id":2764,"question":"Si X suit une loi binomiale de paramètres n=5 et p=0,2, quelle est la probabilité P(X=2) ?","option_a":"0,2048","option_b":"0,3072","option_c":"0,2627","option_d":"0,1638","option_e":"","option_f":"","bonne_reponse":"b","explication":"La formule de la loi binomiale est P(X=k) = C(n,k) * p^k * (1-p)^(n-k). Ici, C(5,2) * (0,2)^2 * (0,8)^3 = 10 * 0,04 * 0,512 = 0,2048.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"0,2048\", \"b\": \"0,3072\", \"c\": \"0,2627\", \"d\": \"0,1638\"}}","_debug_options_count":4},{"id":2765,"question":"Quelle est l'espérance d'une variable aléatoire X suivant une loi de Bernoulli de paramètre p=0,7 ?","option_a":"0,3","option_b":"0,7","option_c":"1","option_d":"0,5","option_e":"","option_f":"","bonne_reponse":"b","explication":"Pour une loi de Bernoulli, l'espérance E(X) est égale à p. Ici, E(X) = 0,7.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"0,3\", \"b\": \"0,7\", \"c\": \"1\", \"d\": \"0,5\"}}","_debug_options_count":4},{"id":2766,"question":"Dans un jeu de pile ou face équilibré, quelle est la probabilité d'obtenir exactement 3 piles en 5 lancers ?","option_a":"0,3125","option_b":"0,25","option_c":"0,15625","option_d":"0,625","option_e":"","option_f":"","bonne_reponse":"a","explication":"C'est une loi binomiale avec n=5 et p=0,5. P(X=3) = C(5,3) * (0,5)^3 * (0,5)^2 = 10 * 0,125 * 0,25 = 0,3125.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"0,3125\", \"b\": \"0,25\", \"c\": \"0,15625\", \"d\": \"0,625\"}}","_debug_options_count":4},{"id":2767,"question":"Quelle est la variance d'une variable aléatoire X suivant une loi uniforme sur {1, 2, 3, 4, 5} ?","option_a":"2","option_b":"1,67","option_c":"2,5","option_d":"1","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour une loi uniforme discrète, la variance est calculée par Var(X) = (n² - 1)\/12. Ici, n=5, donc Var(X) = (25 - 1)\/12 = 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\": \"2\", \"b\": \"1,67\", \"c\": \"2,5\", \"d\": \"1\"}}","_debug_options_count":4}]