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

The correct option is B

7/30

If first ticket drawn is 5 the only 1 can be picked. if ticket numbered 6 is drawn 2 cases possible:1 and 2.

hence $P\left(E_1\right)=\frac{1}{10}\times \frac{1}{9}$

$P\left(E_2\right)=\frac{1}{10}\times \frac{2}{9}$

$P\left(E_3\right)=\frac{1}{10}\times \frac{3}{9}$

$P\left(E\right)=P\left(E_1\right)+P\left(E_2\right)+P\left(E_3\right)+...P\left(E_6\right)$

$P\left(E\right)=\frac{1}{10}(\frac{2}{9}+\frac{3}{9}+\frac{4}{9}+\frac{5}{9}+\frac{6}{9})=\frac{21}{90}=\frac{7}{30}$