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.