Question

Two squares are chosen at random from the small squares drawn on a chessboard. What is the chance that the two squares chosen have exactly one corner in common?

• A. 0.052
• B. 0.042
• C. 0.048
• D. 0.075

Answer 1

The correct option is C 0.048

Option (c)

If the first square chosen is one of the 4 corner squares, the second square can be chosen in 1 way = 4 $\times$1. If the first square chosen is one of the squares on the sides (other than corners) = 24, the second square can be chosen in 2 ways = 24 $\times$ 2

If the first square is any of the middle squares = 36, the second square can be chosen in 4 ways = 36 $\times$ 4. Total number of ways = 4 + 48 + 144 = 196

Number of ways in which 2 random squares can be selected in a chess board = 64 $\times$ 63

Required probability = $\frac{196}{(64\times 63)}$ = 0.048