Liste des multiples de 9 :
9 - 18 - 27 - 36 - 45 (5 éléments)
Liste des multiples de 8:
8 - 16 - 24 - 32 - 40 - 48 (6 éléments)
Liste des nombres premiers:
2 - 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23 - 29 - 31 - 37 - 41 - 43 - 47 (15 éléments)
probabilité d'un événement: nombre d'issues favorables / nombre total d'issues
Ici, on a 50 issues.
a) A barre: tous les nombres non divisibles par 9:
50 - 5 = 45
P(A barre) = 45/50 = 9/10
b) A inter B: P(A) * P(B) = 9/10 * 6/50 = 54 / 500 = 27/250
c) A union B : P(A) + P(B) - (A inter B) = 5/50 + 6/ 50 - 27/250 = 25/250 + 30/250 - 27/250 = 55/250 - 27/250 = 28/250 = 14/125
d) P(C) = 15/50 = 3/10
e) B union C = P(B) + P(C) - (B inter C)
B inter C = P(B) * P(C) = 6/50 * 15/50 = 90/2500 = 9/250
Donc B union C = 6/50 + 15/50 - 9/250 = 30/250 + 75/250 - 9/250 = 105/250 - 9/250 = 96/250 = 48/125
d) A union C = P(A) + P(C) - (A inter C)
A inter C = 5/50 * 15/50 = 75/2500 = 3/100
Donc A union C = 5/50 + 15/50 - 3/100 = 20/50 - 3/100 = 40/100 - 3/100 = 37/100
