Question

The lottery box contains tickets numbered 1-10. 2 tickets are drawn at random without replacement. The probability that the difference between the numbers on the ticket ≥4 is?

• A. 15/30
• B. 7/30
• C. 14/30
• D. 13/30

Answer 1

Answer: (B), (C)

The correct options are
B 7/30
C 14/30

Sample space $=10\times 9=90$

Possible cases that gives a difference exactly equal to 4,
= {(5,1), (6,1), (6,2), (7,1), (7,2), (7,3), (8,1), (8,2), (8,3), (8,4), (9,1), (9,2), (9,3), (9,4), (9,5), (10,1), (10,2), (10,3), (10,4), (10,5), (10, 6)}

Also, each case can be considered as two separate events, i.e, either (1, 5) or (5, 1).

Hence, total number of favourable outcomes = 42

Probability that difference is ≥4 is,
$=\frac{42}{90}=\frac{14}{30}=\frac{7}{15}$