The numbers 1, 2, 3, 4 are written separately on four slips of paper. The slips are then put in a box and mixed thoroughly.

Two slips are then drawn from the box, one after the other, without replacement. Events A, B, C and D are described as follows:

A : The number on the first slip is greater than the number 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 slip is twice the number on the first slip.

E : The number on the first slip is 3 times that on the second slip.

Find: (a) Which pairs of events are mutually exclusive?

(b) Which of the events are simple events?

(c) Which of the events are compound events?

The slips are drawn without replacement.

Sample space, 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)}

{∵ (1, 1), (2, 2), (3, 3), (4, 4) are not possible}

A: The number on the first slip is greater than that on the second slip.

A = {(2, 1), (3, 1), (3, 2), (4, 1), (4, 2), (4, 3)}

B: The number on the second slip is greater than 2

B = {(1, 3), (1, 4), (2, 3), (2, 4), (3, 4), (4, 3)}

C: The sum of numbers on the two slips is 6 or 7

C = {(2, 4), (3, 4), (4, 2), (4, 3)}

D: The number on the second slip is twice the number on the first slip.

D = {(1, 2), (2, 4)}

E: The number on the first slip is thrice that on the second slip.

E = {(3, 1)}

(a) = {(2, 1), (3, 1), (3, 2), (4, 1), (4, 2), (4, 3)} {(1, 2), (2, 4)} =

∴ A and D are mutually exclusive.

= {(1, 3), (1, 4), (2, 3), (2, 4), (3, 4), (4, 3)} {(3, 1)} =

∴ B and E are mutually exclusive.

= {(2, 4), (3, 4), (4, 2), (4, 3)} {{3, 1)} =

∴ C and E are mutually exclusive.

∴ D and E are mutually exclusive.

(b) E = {(3, 1)} n(E) = 1

∴ E is a simple event.

(c) Event A, B, C and D are compound events.