Two squares are chosen at random on a chessboard (see figure). The probability that they have a side in common is :

Question

Two squares are chosen at random on a chessboard (see figure). The probability that they have a side in common is : (A) (2/7) (B) (1/18) (C) (1/7) (D) (1/9)

Tardigrade Admin · Accepted Answer

Total ways of choosing square = 64 C 2 =(64 × 63/2 × 1)=32 × 63 ways of choosing two squares having common side =2(7 × 8)=112 Required probability =(112/32 × 63)=(16/32 × 9)=(1/18)

Q. Two squares are chosen at random on a chessboard (see figure). The probability that they have a side in common is :

$\frac{2}{7}$

$\frac{1}{18}$

$\frac{1}{7}$

$\frac{1}{9}$

Total ways of choosing square $=^{64} C_{2}$
$= \frac{64 \times 63}{2 \times 1} = 32 \times 63$
ways of choosing two squares having common side
$= 2 (7 \times 8) = 112$
Required probability $= \frac{112}{32 \times 63} = \frac{16}{32 \times 9} = \frac{1}{18}$