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?

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.


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