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Byju's Answer
Standard XII
Mathematics
Difference of Two Sets
Prove that: (...
Question
Prove that: (1)P(A∪B)=P(A)+P(B)-P(A∩B) (2)P(A∪B∪C)=P(A)+P(B)+P(C)-P(A∩B)-P(B∩C)-P(C∩A)+P(A∩B∩C)
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Similar questions
Q.
If
A
,
B
,
C
are three events show that
P
(
A
∪
B
∪
C
)
=
P
(
A
)
+
P
(
B
)
+
P
(
C
)
−
P
(
A
∩
B
)
−
P
(
b
∩
C
)
−
P
(
C
∩
A
)
+
P
(
A
∩
B
∩
C
)
Q.
If
A
,
B
,
C
are three events, then show that
P
(
A
∪
B
∪
C
)
=
P
(
A
)
+
P
(
B
)
+
P
(
C
)
−
P
(
A
∩
B
)
−
P
(
B
∩
C
)
−
P
(
C
∩
A
)
+
P
(
A
∩
B
∩
C
)
Q.
If
P
(
A
)
=
1
2
,
P
(
B
)
=
1
3
,
P
(
C
)
=
1
2
a
n
d
P
(
A
∩
B
)
=
P
(
B
∩
C
)
=
P
(
C
∩
A
)
=
1
4
a
n
d
P
(
A
∩
B
∩
C
)
=
1
8
then find
P
(
A
∪
B
∪
C
)
.
Q.
If
P
(
A
)
=
0.7
,
P
(
B
)
=
0.55
,
P
(
C
)
=
0.5
,
P
(
A
∩
B
)
=
x
,
P
(
A
∩
C
)
=
0.45
,
P
(
B
∩
C
)
=
0.3
and
P
(
A
∩
B
∩
C
)
=
0.2
, then
Q.
Let A, B, C be three events such that :
P
(
A
)
=
0.3
,
P
(
B
)
=
0.4
,
P
(
C
)
=
0.5
,
P
(
A
∩
B
′
)
=
0.2
,
P
(
B
∩
C
)
=
0.3
,
P
(
A
′
∩
B
′
∩
C
′
)
=
0.3
and
P
(
A
∩
B
|
C
′
)
=
0.1
. Find the value of
P
(
B
′
|
C
′
)
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