Given: E1 and E2 are two events such that P(E1) =
1
4
and P(E2) =
1
3
and
P(E1 ∪
E2) =
1
2
To show: E1 and E2 are independent events.
We know that,
Hence, P(E1 ∩ E2) = = P(E1) + P(E2) - P(E1 ∪
E2)
=
1
4
+
1
3
−
1
2
=
1
12
Equation 1
Since The condition for two events to be independent is
P(E1 ∩ E2) = P(E1) x P(E2)
=
1
4
×
1
3
=
1
12
Equation 2
Since, Equation 1 = Equation 2
⇒
E1 and E2 are independent events.
Hence proved.
