Томусяк А.А., Трохименко В.С. Теорія ймовірностей
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A
0 6 P (A) 6 1.
n
a
q
m
◦
1, 2, . . . , 9
N
n
M
•
•
•
•
•
Ω
A B
Ω
A B
A B
A B
A + B
A B
A B
·
A · B AB
A A
A B
A· B = ∅ A· B = ∅
A + B = Ω
A
1
A
2
A
3
A
4
A
1
A
2
A
3
A
4
A
1
A
2
A
1
A
3
A
1
A
4
A
3
A
4
A
1
A
2
A
3
A
4
A
1
A
2
A
3
A
4
A
1
+ A
2
A
1
A
3
A
1
A
2
¤
A
B
i i
i = 1, 2, 3 C
C C A A B
i
B
i
1 2
3
C = A + B
1
B
2
B
3
.
1 2 3
1 2 3
C = A(B
1
+ B
2
+ B
3
).
B
1
+ B
2
+ B
3
= B
1
B
2
B
3
C = A · B
1
B
2
B
3
. ¤
1
◦
A
P (A) > 0
2
◦
P (Ω) = 1
3
◦
A B
P (A + B) = P (A) + P (B).
A
A
P (A) = 1 − P (A) P (A) = 1 − P (A).
A A
P (A + A) = P (A) + P (A).
A + A = Ω
P (A) + P (A) = 1.
¤
A B
A B
A ⊂ B
P (A) 6 P (B).
A B
A
B
B A B
A AB
P (B) = P (A) + P (AB).
P (B) − P (A) = P (AB) > 0
P (A) 6 P (B). ¤
A
0 6 P (A) 6 1.
A B
P (A + B) = P (A) + P (B) − P (AB).
A B
P (AB) = 0
A B
A B
A
A B A B
A AB
B
A B A
B B AB
AB
P (A + B) = P (A) + P (AB) P (B) = P (AB) + P (AB).
P (AB)
¤
A, B, C
P (A + B + C) = P (A) + P (B) + P (C).
P (A + B + C) = P (A) + P (B) + P (C) −
− P (AB) − P (BC) − P (AC) + P (ABC).
A
A
1
A
2
A
3
A
A
1
A
2
A
3
A = A
1
+ A
2
+ A
3
.