Question
Given that the two numbers appearing on throwing two dice are different. Find the probability of the event ‘the sum of numbers on the dice is 4’.
Solution
Here 
Number of elements (outcomes) of the above sample space is 6 × 6 = 36.
Let E : the sum of numbers on the dice is 4
∴ E = {(1, 3), (2, 2), (3, 1)}
and F : numbers appearing on the two dice are different
∴ F contains all the points of S except (1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6).
∴ F contains 30 elements.
Also E ∩ F = {(1, 3), (3, 1)}
Required probability = 
