Given: E1 and E2 are two events such that P(E1) =
1
3
and P(E2) =
3
5
To Find:
(i) P(E1 ∪ E2) when E1 and E2 are mutually exclusive.
We know that,
When two events are mutually exclusive P(E1 ∩ E2) = 0
Hence, P(E1 ∪ E2) = P(E1) + P(E2)
=
1
3
+
3
5
=
14
15
Therefore , P(E1 ∪ E2) =
14
15
when E1 and E2 are mutually exclusive.
(ii) P(E1 ∩ E2) when E1 and E2 are independent.
We know that when E1 and E2 are independent ,
P(E1 ∩ E2) = P(E1) x P(E2)
=
1
3
×
3
5
=
1
5
Therefore, P(E1 ∩ E2) =
1
5
when E1 and E2 are independent.
