Given: A and B are the events such that P(A) =
1
2
and P(B) =
7
12
and
P(not A or not B) =
1
4
To Find:
(i) If A and B are mutually exclusive
Since P(not A or not B) =
1
4
i.e., P(
¯
A
∪
¯
B
)
=
1
4
we know that , P(
¯
A
∪
¯
B
)
) = P(A ∩ B)' = 1 - P(A ∩ B) = 0
But here P(A ∩ B) ≠
0
Therefore , A and B are not mutually exclusive.
(ii) If A and B are independent
The condition for two events to be independent is given by
P(E1 ∩ E2) = P(E1) x P(E2)
=
1
2
×
7
12
=
7
24
Equation 2
Since Equation 1 ≠
Equation 2
⇒
A and B are not independent