Question

If two squares are chosen at random on a chess board , then the probability that they have a side in common is
1) 1/9
2) 2/7
3)1/18
4)1/12

Answer 1

In each row we have 7 pairs of squares having a common side.Therefore, totally 8*7 = 56 such squares horizontally. Similarly, we get 56 such squares vertically. So, total number of favourable cases = 56+56=112.  
Required probability = number of favourable outcomes / total no. of possible outcomes

where,number of favourable outcomes= 112*2

and total no. of possible outcomes = 64*63

therefore,probability = 112*2/(64*63)

= 1/18 (after simplification)

so,the answer is 3) 1/18