Two small squares on a chess board are chosen at random. Probability that they have a common side is

1/18

There are 64 small squares on a chessboard.

⇒ Total number of ways to choose two squares = ${^{64}C}_2 = 32.63$

For favourable ways we must choose two consecutive small squares for any row or any columns

⇒ Number of favorable ways = (7.8)2

⇒ Required probability = $\frac{7.8.2}{32.68}=\frac{1}{18}$.