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Byju's Answer
Standard X
Mathematics
Impossible Event
If P A =34, P...
Question
If P(A) =
3
4
,
P
(
B
'
)
=
1
3
and
P
(
A
∩
B
)
=
1
2
then find P(A
∪
B).
Open in App
Solution
Given:
P(A) =
3
4
,
P
(
B
'
)
=
1
3
and
P
(
A
∩
B
)
=
1
2
We know:
P(B) = 1
-
P(B')
= 1-
1
3
=
2
3
On applying the addition theorem of probability, we get:
P(A
∪
B) = P(A) + P(B)
-
P(A
∩
B)
=
3
4
+
2
3
-
1
2
=
9
+
8
-
6
12
=
11
12
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0
Similar questions
Q.
Find P(AUB) when 2P(A)=P(B)=
5
13
and P(A|B)=
2
5
.
Q.
If P(A) = 0.2, P(B’) = 0.6 and P(A
∩
B)= 0.1. Find P(A
∪
B).
Q.
If
P
(
A
)
=
7
13
,
P
(
B
)
=
9
13
,
P
(
A
∪
B
)
=
12
13
,
then find (A|B).
Q.
If A and B are two events such that
i
P
A
=
1
3
,
P
B
=
1
4
and
P
A
∪
B
=
5
12
,
then
find
P
A
|
B
and
P
B
|
A
.
ii
P
A
=
6
11
,
P
B
=
5
11
and
P
A
∪
B
=
7
11
,
then
find
P
A
∩
B
,
P
A
|
B
and
P
B
|
A
.
iii
P
A
=
7
13
,
P
B
=
9
13
and
P
A
∩
B
=
4
13
,
then
find
P
A
|
B
.
iv
P
A
=
1
2
,
P
B
=
1
3
and
P
A
∩
B
=
1
4
,
then
find
P
A
|
B
,
P
B
|
A
,
P
A
|
B
and
P
A
|
B
.
[NCERT EXEMPLAR]
Q.
If
P
(
A
)
=
7
13
,
P
(
B
)
=
9
13
and
P
(
A
∩
B
)
=
4
13
, then the value of
P
(
A
/
B
)
is:
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