Question

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

• A. $\frac{1}{3}$
• B. $\frac{1}{9}$
• C. $\frac{1}{18}$
• D. None of these

Answer 1

The correct option is C $\frac{1}{18}$

There are $64$ small squares on a chess board.

$\Rightarrow$ Total number of ways to choose two squares ${=}^{64}{C}_2=32\times 63$

For favorable ways we must choose two consecutive small squares for any row or any column

$\Rightarrow$ number of favorable ways $=(7\times 8)2$

$\Rightarrow$ Required probability $=\frac{7\times 8\times 2}{32\times 63}=\frac{1}{18}$