1 Expériences aléatoires

o
Ω Ω
ω
Ω
Ω = {P, F }
2
Ω = {1,2,...,6}
ω=
(ω1, ω2)ω1ω2
Ω = {1,2,...,6}2
C
32 8
Ω = {P⊂ C : Card(P)=8}
C8

Ω = {AA, Aa, aa}
5 (ω1, . . . , ω5)
J
Ω = {5−J}
(1) (2) (3)
(4)
Ω = { {1,2,3,4}} ={(1,2,3,4),(2,1,3,4), . . .}
Card(Ω)
Ω = {1,2,3, . . .}=N∗
Ω = [0,+∞[= R∗
Ω
Ω
E
Ωω
ω∈E ω
ω /∈E

EΩ
P(Ω) A ω
A
P(Ω)
Ω
Ω
∅
E={ω}
A⊂B A B
E
E={2,4,6}
Ω = {1,2,...,6}2F
F={(1,1),(2,2),...,(6,6)},
G5
G={(1,4),(2,3),(3,2),(4,1)},
H6
H={(6,6)}.
6
M≤4G
M M G
A B
•A A A
•A∪B A B A B
•A∩B A B A B

A∩B=∅A B
Ω = {1,2,...,6}A
3B≤2
∪ ∩
(A∪B) = A∩B, (A∩B) = A∪B
A∪B=B∪A, A ∩B=B∩A
∪ ∩
A∪(B∩C)=(A∪B)∩(A∪C), A∩(B∪C) = (A∩B)∪(A∩C)
A∪∅=A, A ∩∅=∅, A ∪Ω = Ω, A ∩Ω = A
(A1, . . . , An)
∀i, j ∈ {1,2, . . . , n}i6=j Ai∩Aj=∅
Sn
i=1 Ai= Ω
Ai
Ω = {1,2,...,100}A={1,2,...,20}
B={21,...,50}C={51,...,100}(A, B, C)
Ω

Ω = {1,2,...,6}2
A B C
(A, B, C)
Ω
A(A, A)
A∩A=∅A∪A= Ω
0 1
Ω
P:P(Ω) →[0,1]
A7→ P(A)
A B A ∩B=∅
P(A∪B) = P(A) + P(B)