Correct Answer - D
We have,
P(Exactly one of A, B occurs)
=
P
[
(
A
∩
¯¯¯
B
)
∪
(
¯¯¯
A
∩
B
)
]
=
=
P
(
A
∩
¯¯¯
B
)
+
P
(
¯¯¯
A
∩
B
)
=
=
P
(
A
)
−
P
(
A
∩
B
)
+
P
(
B
)
−
P
(
A
∩
B
)
=
=
P
(
A
)
+
P
(
B
)
−
2
P
(
A
∩
B
)
=
P
(
A
∩
B
)
−
P
(
A
∩
B
)
=
Also,
P, (Exactly one of A, B occurs)
=
P
(
A
∪
B
)
−
P
(
A
∩
B
)
=
=
{
1
−
P
(
¯¯¯¯¯¯¯¯¯¯
A
∪
B
)
}
−
{
1
−
P
(
¯¯¯¯¯¯¯¯¯¯
A
∩
B
)
}
=
=
[
1
−
P
(
¯¯¯
A
∩
¯¯¯
B
)
]
−
[
1
−
P
(
¯¯¯
A
∪
¯¯¯
B
)
]
=
=
P
(
¯¯¯
A
∪
¯¯¯
B
)
−
P
(
¯¯¯
A
∩
¯¯¯
B
)
=
P
(
¯¯¯
A
)
+
P
(
¯¯¯
B
)
−
2
P
(
¯¯¯
A
∩
¯¯¯
B
)
=
.
Hence, option (d) is incorrect.
