Question

From the set of numbers $\{1,2,3,4,5,6,7,8\}$ two numbers are selected at random without replacement. The probability that their sum is more than $13$ is

• A. $\frac{1}{14}$
• B. $\frac{2}{7}$
• C. $\frac{3}{7}$
• D. $\frac{4}{7}$

Answer 1

The correct option is A $\frac{1}{14}$

The sample space for given condition is

$(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,8)$

$(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)$

$(1,6),(2,6),(3,6),(4,6),(5,6)$

$(1,5),(2,5),(3,5),(4,5)$

$(1,4),(2,4),(3,4)$

$(1,3),(2,3)$

$(1,2)$

Number of sample space is 28.

Number of sample space where the sum of two numbers is more than 13 is $2\left(\right(6,8),(7,8\left)\right)$. Therefore the probability is $\frac{2}{28}=\frac{1}{14}$