The numbers 1, 2, 3 and 4 are written separately on four slips of paper. The slips are then put in a box and mixed thoroughly. A person draws two slips from the box, one after the other, without replacement. Describe the following events:
A = The number on the first slip is larger than the one on the second slip.
B = The number on the second slip is greater than 2
C = The sum of the numbers on the two slips is 6 or 7
D = The number on the second slips is twice that on the first slip.
Which pair(s) of events is (are) mutually exclusive?
Solution
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)}
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)}
B = number on the second slip is greater than 2
={(1, 3), (2, 3), (1, 4), (2, 4), (3, 4), (4, 3)}
C = sum of the numbers on the two slips is 6 or 7
={(2, 4), (3, 4), (4, 2), (4, 3)}
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.
