Four slips marked as 1, 2, 3 and 4 are in a box. Two slips are drawn from it one after the other without replacement. The sample space S for the experiment is
S = {(1, 2), (1, 3), (1, 4), (2, 1), (2, 3), (2, 4), (3, 1), (3, 2), (3, 4), (4, 1), (4, 2), (4, 3)}
(i) A = number on the first slip is larger than the one on the second slip
= {(2, 1), (3, 1), (3, 2), (4, 1), (4, 2), (4, 3)}
(ii) B = number on the second slip is greater than 2
={(1, 3), (2, 3), (1, 4), (2, 4), (3, 4), (4, 3)}
(iii) C = sum of the numbers on the two slips is 6 or 7
={(2, 4), (3, 4), (4, 2), (4, 3)}
(iv) D = number on the second slip is two times the number on the first slip
= {(1, 2), (2, 4)}
Clearly, (A ∩ D) = Φ
Therefore, A and D are mutually exclusive events.