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:

Question

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?

Philoid · Accepted Answer

Given: There are 4 slips in the box and mixed thoroughly.

To Find: Describe the given events .

Explanation: 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.