Example 10 A die is thrown If E is the event ‘the number appearing is a multiple of
3’ and F be the event ‘the number appearing is even’ then find whether E and F are
independent Solution We know that the sample space is S = {1, 2, 3, 4, 5, 6}
Now
E = { 3, 6}, F = { 2, 4, 6} and  E ∩ F = {6}
Then
P(E) = 2
1
3
1
1
, P(F)
and P(E
 F)
6
3
6
2
6
=
=
=
∩
=
Clearly
P(E ∩ F) = P(E) P (F)
Hence
E and F are independent events