Formule des probabilités totales

A1, . . . , An
Akp
Ak+1 1−p
pnAn
A1
0<p<1pnn

Aii
B1, . . . , B4
A1∩A2, A1∩¯ A2,¯ A1∩A2¯ A1∩¯ A2
P(A3) =
4
X
k=1
P(A3|Bk) P(Bk)
P(A3|B1) = 0
P(A3|B2) = P(A3|B3) = 1/8 P(B2) = P(B3)=8/10 ×2/9
P(A3|B4)=2/8 P(B4)=8/10 ×7/9
P(A3) = 2
5×1 9+1 5×7 9=9 45 =1 5
p1= 1 p2=p
pnAnA1
pn+1 =ppn+ (1 −p)(1 −pn)
(pn)
pn+1 = (2p−1)pn+ 1 −p
p1= 1
pn=1 + (2p−1)n−1
2
p∈]0 ; 1[ |2p−1|<1pn→1/2