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?

Answer 1

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.