Solution If all the 36 elementary events of the experiment are considered to be equally
likely, we have
P(A) = 18
1
36
=2
 and 
18
1
P(B)
36
2
 
 
Also
P(A ∩ B) = P (odd number on both throws)
= 9
1
36
4
=
Now
P(A) P(B) = 1
1
1
2
2
4
×
=
Clearly
P(A ∩ B) = P(A) × P(B)
Thus,
A and B are independent events
Example 12 Three coins are tossed simultaneously Consider the event E ‘three heads
or three tails’, F ‘at least two heads’ and G ‘at most two heads’ Of the pairs (E,F),
(E,G) and (F,G), which are independent which are dependent