GrowGen
给我
整
Home
Blog
Lab
World
Archive
Search...
⌘
+
K
2021-08-31
概率论的基本公式
book
概率论
#math
Headings
概率论的基本公式
Tags
book
math
概率论
book
math
概率论
概率论的基本公式
J.Gong
2021-08-31
0.63min
概率论的基本公式
A
⊂
B
,
P
(
B
−
A
)
=
P
(
B
)
−
P
(
A
)
A \subset B,P(B-A)=P(B)-P(A)
A
⊂
B
,
P
(
B
−
A
)
=
P
(
B
)
−
P
(
A
)
P
(
A
∪
B
)
=
P
(
A
)
+
P
(
B
)
−
P
(
A
B
)
P(A \cup B) = P(A) + P(B) -P(AB)
P
(
A
∪
B
)
=
P
(
A
)
+
P
(
B
)
−
P
(
A
B
)
P
(
A
1
∪
A
2
∪
A
3
)
=
P
(
A
1
)
+
P
(
A
2
)
+
P
(
A
3
)
−
P
(
A
1
A
2
)
−
P
(
A
1
A
3
)
−
P
(
A
2
A
3
)
+
P
(
A
1
A
2
A
3
)
P(A_1 \cup A_2 \cup A_3) = P(A_1) + P(A_2) + P(A_3) - P(A_1A_2) - P(A_1A_3) - P(A_2A_3) + P(A_1A_2A_3)
P
(
A
1
∪
A
2
∪
A
3
)
=
P
(
A
1
)
+
P
(
A
2
)
+
P
(
A
3
)
−
P
(
A
1
A
2
)
−
P
(
A
1
A
3
)
−
P
(
A
2
A
3
)
+
P
(
A
1
A
2
A
3
)
P
(
A
1
∪
A
2
∪
A
3
∪
A
4
)
=
P
(
A
1
)
+
P
(
A
2
)
+
P
(
A
3
)
+
P
(
A
4
)
−
[
P
(
A
1
A
2
)
+
P
(
A
1
A
3
)
+
P
(
A
1
A
4
)
+
P
(
A
2
A
3
)
+
P
(
A
2
A
4
)
+
P
(
A
3
A
4
)
]
+
[
P
(
A
1
A
2
A
3
)
+
P
(
A
1
A
2
A
4
)
+
P
(
A
1
A
3
A
4
)
+
P
(
A
2
A
3
A
4
)
]
+
P
(
A
1
A
2
A
3
A
4
)
P(A_1 \cup A_2 \cup A_3 \cup A_4) = P(A_1) + P(A_2) + P(A_3) + P(A_4) - [ P(A_1A_2) + P(A_1A_3) + P(A_1A_4) + P(A_2A_3) + P(A_2A_4) + P(A_3A_4) ] + [ P(A_1A_2A_3) + P(A_1A_2A_4) + P(A_1A_3A_4) + P(A_2A_3A_4) ] + P(A_1A_2A_3A_4)
P
(
A
1
∪
A
2
∪
A
3
∪
A
4
)
=
P
(
A
1
)
+
P
(
A
2
)
+
P
(
A
3
)
+
P
(
A
4
)
−
[
P
(
A
1
A
2
)
+
P
(
A
1
A
3
)
+
P
(
A
1
A
4
)
+
P
(
A
2
A
3
)
+
P
(
A
2
A
4
)
+
P
(
A
3
A
4
)]
+
[
P
(
A
1
A
2
A
3
)
+
P
(
A
1
A
2
A
4
)
+
P
(
A
1
A
3
A
4
)
+
P
(
A
2
A
3
A
4
)]
+
P
(
A
1
A
2
A
3
A
4
)
P
(
A
−
B
)
=
P
(
A
)
−
P
(
A
B
)
=
P
(
A
B
ˉ
)
P(A-B) = P(A) - P(AB) = P(A\bar{B})
P
(
A
−
B
)
=
P
(
A
)
−
P
(
A
B
)
=
P
(
A
B
ˉ
)
P
(
B
∣
A
)
=
P
(
A
B
)
P
(
A
)
P(B|A) = \frac{P(AB)}{P(A)}
P
(
B
∣
A
)
=
P
(
A
)
P
(
A
B
)
P
(
B
ˉ
∣
A
)
=
1
−
P
(
B
∣
A
)
P(\bar{B}|A) = 1 - P(B|A)
P
(
B
ˉ
∣
A
)
=
1
−
P
(
B
∣
A
)
P
(
B
−
C
∣
A
)
=
P
(
B
∣
A
)
−
P
(
B
C
∣
A
)
P(B-C|A) = P(B|A)-P(BC|A)
P
(
B
−
C
∣
A
)
=
P
(
B
∣
A
)
−
P
(
BC
∣
A
)
P
(
A
B
)
=
P
(
A
)
P
(
B
∣
A
)
P(AB)=P(A)P(B|A)
P
(
A
B
)
=
P
(
A
)
P
(
B
∣
A
)
⋃
i
=
1
n
A
i
=
Ω
,
A
i
A
j
=
Φ
,
B
=
⋃
i
=
1
n
A
i
B
,
P
(
B
)
=
∑
i
=
1
n
P
(
A
)
P
(
B
∣
A
)
\bigcup_{i=1}^n A_i = \Omega, A_iA_j = \Phi, B=\bigcup_{i=1}^n A_iB, P(B) = \sum^n_{i=1}P(A)P(B|A)
i
=
1
⋃
n
A
i
=
Ω
,
A
i
A
j
=
Φ
,
B
=
i
=
1
⋃
n
A
i
B
,
P
(
B
)
=
i
=
1
∑
n
P
(
A
)
P
(
B
∣
A
)
⋃
i
=
1
n
A
i
=
Ω
,
A
i
A
j
=
Φ
,
P
(
A
j
∣
B
)
=
P
(
A
j
)
P
(
B
∣
A
j
)
∑
i
=
i
n
P
(
A
i
)
P
(
B
∣
A
i
)
\bigcup_{i=1}^n A_i = \Omega, A_iA_j = \Phi, P(A_j|B)=\frac{P(A_j)P(B|A_j)}{\sum^n_{i=i}P(A_i)P(B|A_i)}
i
=
1
⋃
n
A
i
=
Ω
,
A
i
A
j
=
Φ
,
P
(
A
j
∣
B
)
=
∑
i
=
i
n
P
(
A
i
)
P
(
B
∣
A
i
)
P
(
A
j
)
P
(
B
∣
A
j
)
P
(
A
B
ˉ
)
=
P
(
A
ˉ
∪
B
ˉ
)
P(\bar{AB})=P(\bar{A} \cup \bar{B})
P
(
A
B
ˉ
)
=
P
(
A
ˉ
∪
B
ˉ
)
