Question

The number 1, 2, 3 and 4 are written separately on four slips of paper. The slips arc 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 second slip is greater than 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.

Answer 1

Four slips marked as 1, 2, 3 and 4 are in a box Two slips are drawn from it one after the other without replacement. The sample space S 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

$A\cup F$ = {(2,1),(3, 1), (3,2), (4,1), (4,2), (4,3)}

(ii) B = number on the second slip is greater than 2
={(1,3),(2, 3),(1,4),(2.4),(3,4), (4,3)}

(iii) C = sum of the numbers on the two slips is 6 or 7
= {(2, 4), (3, 4), (4, 2), (4, 3)}

(iv) D= number on the second slip is two times the number on the first slip
= {(1, 2), (2, 4)}
Clearly, $(A\cap D)=\varphi$

Therefore, A and D are mutually exclusive events.