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?

Here, four slips of paper 1, 2, 3, and 4 are put in a box.

If Two slips are drawn from it one after the other without replacement. Then

The sample space 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,

So, the sample space for A is:

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

(ii) B = number on the second slip is greater than 2

So, the sample space for B is

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

(iii) C = sum of the numbers on the two slips in 6 or 7

The sample space for C is

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

(iv) D = number on the second slip is two times the number on the first slip

The sample space if:

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

Now,

We can see, AՌD = Փ

Therefore, A and D are mutually exclusive events

Hence, A and D are mutually exclusive events.