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
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B
0.042
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C
0.048
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D
0.075
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Solution

## The correct option is B 0.048Option (c) If the first square chosen is one of the 4 corner squares, the second square can be chosen in 1 way = 4 ×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 × 2 If the first square is any of the middle squares = 36, the second square can be chosen in 4 ways = 36 × 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 × 63 Required probability = 196(64×63) = 0.048

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