1 Définitions et exemples - LMPA

ω ω1ω2
ωiP(ωi)ωi
P(ωi)ωi
0≤P(ωi)≤1 1
A
A
1,2,...,10
1
P(ωi) 1/10
A={4,5,6}.
P(A) = P(4) + P(5) + P(6) = 1
10 +1 10 +1 10 =3 10 .
4A7A
(1,1),(1,2),(2,1),...,(6,6)
1P(ωi) 1/36
4
A={(1,3),(2,2),(3,1)}.
P(A) = P((1,3)) + P((2,2)) + P((3,1)) = 1
36 +1 36 +1 36 =3 36 =1 12 .
(1,3) A(2,5) A

p fp ffp fff p
fp ffp fff
P(p)=1/2P(fp)=1/4P(ffp) = P(fff)=1/8
P(ωi)
A={p, fp, ffp}.
P(A) = P(p) + P(fp) + P(ffp) = 1
2+1 4+1 8=7 8.
A B
A∩B A ∩B A B
A={4,5,6}B
B={4,5,7,8,9,10}A∩B={4,5}.
A={(1,3),(2,2),(3,1)}B
B={(2,1),(2,2),...,(2,6)}A∩B={(2,2)}.
A={p, fp, ffp}B
B={ffp, fff}A∩B={ffp}.
A B
A B
A PB(A)
PB(A) = P(A∩B)
P(B).
A
PB(A) = P(A∩B)
P(B)=2/10 6/10 =2 6.
A
PB(A) = P(A∩B)
P(B)=1/36 6/36 =1 6.
A
PB(A) = P(A∩B)
P(B)=1/8 2/8=1 2.

C1C2
C1
C2C1
C1
C1
C1
C1C2