Question

Two numbers are selected randomly from the set $S = \{1, 2, 3, 4, 5, 6\}$ without replacement. The probability that minimum of the two numbers is less than $4$, is

• A. $\frac{1}{15}$
• B. $\frac{14}{15}$
• C. $\frac{1}{5}$
• D. $\frac{4}{5}$

Answer 1

Answer: (D)

Here, two numbers are selected from $\{1,2,3,4,5,6\}$ $\Rightarrow n(S)=6 \times 5 \{$ as one by one without replacement $\}$
Favourable events $=$ the minimum of the two numbers is less than $4 .$
$n(E)=6 \times 4$ as for the minimum of the two is less than $4$ we can select one from $(1,2,3,4)$ and other from $(1,2,3$, $4,5,6)$
$\therefore$ Required probability $=\frac{n(E)}{n(S)}=\frac{24}{30}=\frac{4}{5}$