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

Answer: (A)

$\frac{1}{14}$

We may choose $6,8$ and $7,8$ to get the sum more than $13$.
There is no other possible way to choose numbers such that the sum is more than $13$.
Total ways of choosing $2$ numbers $=C_2^8=28$
Favourable cases $=2$
Total cases $=28$
Probability $=\frac{2}{28}=\frac{1}{14}$
So, A is the correct answer.