Conditionnement

B A
E E
A B E P(A)6= 0
B A
PA(B) = P(A∩B)
P(A)
B
A
A B E P(A)6= 0
•0≤PA(B)≤1
•PA(B) + PA(B)=1
•
PA(B) = B∩A
A

PA(B)B
AP(A∩B)A B
•P(A∩B) = P(A)×PA(B)P(A)6= 0
•P(A∩B) = P(B)×PB(A)P(B)6= 0
A A
BP(A∩B)P(A∩B)P(B)
BP(A∩B)P(A∩B)P(B)
P(A)P(A) 1
PA(B)P(A∩B)P(A)
A B P(A∩B)=0.18 P(A∩B)=0.42
P(A) = P(A∩B) + P(A∩B)=0.18 + 0.42 = 0.6
P(A)=1−P(A)=1−0.6=0.4
A A
B0.18 0.1 0.28
B0.42 0.3 0.72
0.6 0.4 1
PA(B) = 0.25
P(A∩B) = P(A)×PA(B)=0.4×0.25 = 0.1
P(A∩B) = 0.4−0.1 = 0.3

E
A A
•1
•
•

A1A2. . . An
E
E
B
P(B) = P(A1∩B) + P(A2∩B) + . . . +P(An∩B)
P(B) = P(A1)×PA1(B) + P(A2)×PA2(B) + . . . +P(An)×PAn(B)
A1A2A3P(A1) +
P(A2) + P(A3) = 1 E
B

B
P(B) = P(A1∩B) + P(A2∩B) + P(A3∩B)
B
P(B) = P(A1)×PA1(B) + P(A2)×PA2(B) + P(A3)×PA3(B)
A B E P(A)6= 0
P(B) = P(A∩B) + P(A∩B)
P(B) = P(A)×PA(B) + P(A)×PA(B)