Chapitre 3 : Introduction aux probabilités

Ω
Ω = {1,2,3,4,5,6}
{2,4,6}
A∪B
A∩B
A
∅
A={2,4,6}=
B={4,5,6}=
A∪B={2,4,5,6}
A∩B={4,6}
A={1,3,5}=
A
P(A)
P(A)
P(A) = 0 AP(A) = 1 A
pi=i=P({i})

P(A) = ∑
i∈A
pi=A
i
pi
P( ) = P({4,5,6}) = p4+p5+p6= 0,7.
1
nn=|Ω|=
P(A) = |A|
|Ω|=
Ω = {1,2,3,4,5,6}
P( ) = P({4,5,6}) = 3
6= 0,5.
P(∅) = 0
P(Ω) = 1 ∑
i∈Ω
pi= 1
P(A∪B) = P(A) + P(B)−P(A∩B)
A B A ∩B=
P(A∪B) = P(A) + P(B).
P(A) = 1 −P(A)
B A
PA(B) = P(A∩B)
P(A)

PS(V) = 0,2
0,6∼
=0,3333
PA(Ω) = 1
PA(B∪C) = PA(B) + PA(C)−PA(B∩C)
PA(B) = 1 −PA(B)
P(A∩B) = PA(B)P(A)
P(A) = PB(A)P(B) + PB(A)P(B)
PB(A) = PA(B)P(A)
P(B)
H F P(H)=0,6
PH(F) = 0,3PH(F) = 0,4
P(H∩F) = P(H)×PH(F) = 0,6×0,3 = 0,18
P(F) = 0,6×0,3 + (1 −0,6) ×0,4 = 0,34
PF(H) = 0,6×0,3
0,34 ∼
=0,53
P(A∩B) = P(A)P(B)
PB(A) = P(A)

A={ ≥ 3}
B={ ≥ 4}
P(A∩B) = 4
6×3 6=1 3
A={ ≤ 4}B={ }
P(A) = 2
3P(B) = 1 2P(A)×P(B) = 1 3
P(A∩B) = 2
6=1 3
P(A∩B) = P(A)P(B)
(A∪B) = A∪B(A∪B) = A∩B
(A∪B)∩C= (A∩C)∪(B∩C) (A∪B)∩C=A∪(B∩C)

A A ∩B B ∩C A ∩B∩C A ∪B B ∪C A ∩B∪C
A B C
P(A∩D)P(A∩D)