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Question: What is the probability that the two squares chose randomly on a chess board, share a side -...

What is the probability that the two squares chose randomly on a chess board, share a side -

A

1/18

B

13/254

C

105/288

D

13/96

Answer

1/18

Explanation

Solution

Total no. of selection of 2 squares out of 64 squares on a chess board = 64C2 = 32 × 63 the no. of ways of selecting two consecutive squares from rows or from columns = (7 + 7 + … to 8 terms) + (7 + 7 + …. to 8 terms) = 56 + 56 = 112

Probability = 11232.63\frac { 112 } { 32.63 } = 118\frac { 1 } { 18 }