A board has 16 squares as shown in the figure :  

Out of these 16 squares, two squares are chosen at random. The probability that they have no side in common is : 
 

Total ways for selecting any two squares ${=}^{16}{\mathrm{C}}_2=120$
Total ways for selecting common side squares $=\underset{\text{Horizontal side }}{\underbrace{3\times 4}}+\underset{\text{vertical side }}{\underbrace{3\times 4}}$= 24
so required probability $=1-\frac{24}{120}=\frac{4}{5}$