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NDA Math Probability Part 2
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© examsnet.com
Question : 38
Total: 59
If
A
and
B
are two events such that
P
(
A
)
=
0.6
,
P
(
B
)
=
0.5
and
P
(
A
∩
B
)
=
0.4
,
then consider the following statements:
1.
P
(
A
∪
B
)
=
0.9
.
2.
P
(
B
|
A
)
=
0.6
Which of the above statements is/are correct?
[NDA-I 2020]
1 only
2 only
Both 1 and 2
Neither 1 nor 2
Validate
Solution:
👈: Video Solution
P
(
−
A
)
=
1
−
P
(
A
)
=
1
−
0.6
=
0.4
P
(
B
)
=
1
−
P
(
B
)
=
1
−
0.5
=
0.5
Now,
P
(
A
∪
B
)
=
P
(
A
)
+
P
(
B
)
−
P
(
A
∩
B
)
=
0.6
+
0.5
−
0.4
=
0.7
(1)
Now
P
(
A
∪
B
)
=
P
(
A
)
+
P
(
B
)
−
P
(
A
∩
B
)
=
P
(
A
)
+
P
(
B
)
−
{
P
(
B
)
−
P
(
A
∩
B
)
}
=
0.4
+
0.5
−
{
0.5
−
0.4
}
=
0.8
Hence, statement (1) is not correct.
(2)
P
(
B
∣
A
)
=
P
(
B
∩
A
)
P
(
A
)
=
P
(
B
∪
A
)
′
P
(
A
)
=
1
−
P
(
A
∪
B
)
P
(
A
)
=
1
−
0.7
0.4
=
0.75
Hence, statement (2) is not correct.
© examsnet.com
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