Question

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

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

Answer 1

The correct option is D $\frac{4}{5}$

Here, two number are selected from $\{1,2,3,4,5,6\}$
$\Rightarrow n\left(S\right)=6\times 5$ $($as one by one without replacement$)$

Favourable events $=$ the minimum of the two number is less than $4$
$n\left(E\right)=6\times 4$

$($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 $=\frac{n\left(E\right)}{n\left(S\right)}=\frac{24}{30}=\frac{4}{5}$