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

$\frac{4}{5}$

The minimum of two numbers is less than 4 means at least one of them is less than 4.

Let $A_i$ denote the event that the number selected in $i^{th}$ draw is less than 4, where i = 1, 2. Then,

Required probability =$P(A_1 ∪ A_2) = 1- P(\overline{A_1}∩\overline{A_2})$

$= 1- P(\overline{A_1})P(\overline{A_2}/\overline{A_1})= 1 -\frac{3}{6}× \frac{2}{5}=\frac{4}{5}$