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JEE Main 26-Aug-2021 Shift 1 Solved Paper
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© examsnet.com
Question : 65
Total: 90
Let A and B be independent events such that
P
(
A
)
=
p
and
P
(
B
)
=
2
p
. The largest value of p, for which P (exactly one of A, B occurs)
=
5
9
, is
[26 Aug 2021 Shift 1]
1
3
2
9
4
9
5
12
Validate
Solution:
P( Exactly one out of A or B occurs )
=
5
9
p
(
A
⋂
B
)
+
p
(
A
⋂
B
)
=
5
9
p
(
A
)
p
(
B
)
+
p
(
A
)
p
(
B
)
=
5
9
∴
p
(
1
−
2
p
)
+
(
1
−
p
)
2
p
=
5
9
⇒
9
p
(
1
−
2
p
)
+
18
p
(
1
−
p
)
=
5
⇒
9
p
−
18
p
2
+
18
p
−
18
p
2
=
5
⇒
36
2
p
−
27
p
+
5
=
0
(
3
p
−
1
)
(
12
p
−
5
)
=
0
p
=
1
3
or
p
=
5
12
p
max
=
5
12
© examsnet.com
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