Correct Answer - D
We have,
Required probability
=
P
(
¯¯¯
A
∪
¯¯¯
B
)
=
P
(
¯¯¯¯¯¯¯¯¯¯
A
∩
B
)
=
1
−
P
(
A
∩
B
)
=
So, alternative (a) is correct.
Again,
P
(
¯¯¯
A
∪
¯¯¯
B
)
=
P
(
¯¯¯
A
)
+
P
(
¯¯¯
B
)
−
P
(
¯¯¯
A
∩
¯¯¯
B
)
P
[ By add. Theorem]
So, alternative (b) is correct.
Again,
P
(
¯¯¯
A
∪
¯¯¯
B
)
P
=
P
(
¯¯¯
A
)
+
P
(
¯¯¯
B
)
−
P
(
¯¯¯
A
∩
¯¯¯
B
)
=
=
P
(
¯¯¯
A
)
+
P
(
¯¯¯
B
)
−
P
(
¯¯¯¯¯¯¯¯¯¯
A
∪
B
)
=
=
(
P
(
¯¯¯
A
)
+
P
(
¯¯¯
B
)
−
{
1
−
P
(
A
∪
B
)
}
=
=
P
(
¯¯¯
A
)
+
P
(
¯¯¯
B
)
+
P
(
A
∪
B
)
−
1
=
.
So, alternative (c ) is also correct.
