Table des matières 1 Probabilités conditionnelles

(Ω,A, P )B∈ A P(B)6= 0
(Ω,A, PB)PB(A) = P(A∩B)
P(B)A∈ A
PBB
PB(A)A B P (A|B)
(Ω,A, P )
n∈N∗(Ai)i∈[[1,n]] AP(A1∩ · · · ∩ An−1)6= 0
P(A1∩ · · · ∩ An) = P(A1)PA1(A2)PA1∩A2(A3). . . PA1∩···∩An−1(An)
(Ω,A, P )
I⊂N∗(Ai)i∈IΩ
B∈ A P(B) = X
i∈I
P(B∩Ai)
i∈I P (Ai)6= 0 P(B) = X
i∈I
P(Ai)PAi(B)

(A, B)∈ A2
P(B) = P(A∩B) + PA∩B
P(A)∈]0; 1[ P(B) = P(A)PA(B) + PAPA(B)
P(A)∈]0; 1[⇐⇒ P(A)6= 0 PA6= 0⇐⇒ A;A
(Ω,A, P )A∈ A P(A)∈]0; 1[
B∈ A P(B)6= 0 PB(A) = P(A)PA(B)
P(B)=P(A)PA(B)
P(A)PA(B) + PAPA(B)
(Ω,A, P ) (A, B)∈ A2
A B P (A∩B) = P(A)P(B)
A B P (A∩B) = P(A)P(B)
A B A ∩B=∅
A B P (A∪B) = P(A) + P(B)
(Ω,A, P ) (A, B)∈ A2P(A)6= 0
A B P (B) = PA(B)

(Ω,A, P ) (A, B)∈ A2
A B
A B
A B
A B
(Ω,A, P )I⊂N∗
(Ai)i∈I
(i, j)∈I2, i 6=j=⇒P(Ai∩Aj) = P(Ai)P(Aj)
(Ω,A, P )I⊂N∗
(Ai)i∈I
J⊂I P \
i∈J
Ai!=Y
i∈J
P(Ai)
(Ω,A, P )T S A
T S T∈ T S∈ S
T S
(Ω,A, P )
(Ai)i∈I(Bj)j∈J(i, j)∈I×J AiBj