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Mathematics
Let A and B be two events such that P ( B mid A )=(2/5), P ( A mid B )=(1/7) and P ( A ∩ B )=(1/9). Consider (S1) P ( A prime ∪ B )=(5/6), (S2) P ( A prime ∩ B prime)=(1/18). Then
Q. Let
A
and
B
be two events such that
P
(
B
∣
A
)
=
5
2
,
P
(
A
∣
B
)
=
7
1
and
P
(
A
∩
B
)
=
9
1
. Consider (S1)
P
(
A
′
∪
B
)
=
6
5
, (S2)
P
(
A
′
∩
B
′
)
=
18
1
. Then
2178
0
JEE Main
JEE Main 2022
Probability - Part 2
Report Error
A
Both (S1) and (S2) are true
51%
B
Both (S1) and (S2) are false
16%
C
Only (S1) is true
10%
D
Only (S2) is true
23%
Solution:
P
(
A
∣
B
)
=
7
1
⇒
P
(
B
)
P
(
A
∩
B
)
=
7
1
⇒
P
(
B
)
=
9
7
P
(
B
∣
A
)
=
5
2
⇒
P
(
A
)
P
(
A
∩
B
)
=
5
2
⇒
P
(
A
)
=
18
5
Now,
P
(
A
′
∪
B
)
=
1
−
P
(
A
∪
B
)
+
P
(
B
)
=
1
−
P
(
A
)
+
P
(
A
∩
B
)
=
6
5
P
(
A
′
∩
B
′
)
=
1
−
P
(
A
∪
B
)
=
1
−
P
(
A
)
−
P
(
B
)
+
P
(
A
∩
B
)
=
18
1
⇒
Both (S1) and (S2) are true