Recherche opérationnelle Stochastiques

qk
k(0 ≤k≤4) q0+q1+q2+q3+q4= 1
qk= = k
C13
52 =52!
13!(52 −13)!
k
→k(13 −k)
k Ck
4
(13 −k)C13−k
48
qk=Ck
4C13−k
48
C13
52
,
4
X
k=0
qk= 1
q0=C0
4C13 48
C13
52
=48!
13!35!
13!39!
52! =39 ×38 ×37 ×36 52 ×51 ×50 ×49 ≈0,304
q1≈0,439
q2≈0,213
q3≈0,041
q4≈0,003
Q=C13
26
C13
52
≈1,6.10−5
l≤45mm
l > 45mm
P(C) = 0,75 = q P (L) = 0,25 = p
P(2L, 1C) = ppq +pqp +qpp = 3p2q
n m p (n−m)
q
Cm
npmqn−m
U1U2U1U2

P(2B) = 1
P(2B) = 3
4×3 4
P(2B) = 1
2×1 + 1 2×3 4×3 4=25 32
P(A/B)P(B/A)
P(A/B) = P(B/A)P(A)
P(B)
P(U1/1B) = P(1B/U1)P(U1)
P(1B)=1×1
2
1
2×1 + 1 2
3
4
=4
7
P(U2/1B) = P(1B/U2)P(U2)
P(1B)=
3
4×1 2
1
2×1 + 1 2
3
4
=3
7
P(2emeB/1ereB) = 4
7×1 + 3 7
3
4=25 28
P(2B) = 1
2×1 + 1 2×3 4×23 = 3 4=24 32
P(2emeB/1ereB) = 4
7×1 + 3 7
2
3=24 28
A B C D E
C C
τ= 1s τ

(A, A, B, B, B, . . .) (A, C, C, C, D, D, C, . . .)
Eikτ
P(Ej/Ei)j=0
M n ×n n M
Pi,j =P(etatj/etati)
M=
0,2 0,5 0,3 0 0
0 1 0 0 0
0 0 0,3 0,4 0,3
0 0 0,3 0,7 0
0 0 0 0,4 0,6
M
⇐⇒
(i, j)⇐⇒ i kτ j (k+ 1)τ
(i, j)⇐⇒ Pi,j
32τ
Π32 = (ΠA
32,ΠB 32, . . . , ΠE 32)AΠ0= (1,0,0,0,0)
Πk= Πk−1M, k ≤1
ΠC
1= ΠA 0pA,C + ΠB 0pB,C +. . . + ΠE 0pE,C
Πk