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.