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 numbers is less than  4is

 The minimum of two numbers will be less than 4 or at least one of the numbers is less than 4. 

Therefore, 

$\begin{array}{c}P(\text{ at least one numbers }<4)=1-P(\text{ both the numbers }\ge 4)\\ =1-\frac{3}{6}\times \frac{2}{5}\\ =1-\frac{6}{30}\\ =1-\frac{1}{5}=\frac{4}{5}\end{array}$