Interpret the figure

A board with $16$ squares "as shown" is naturally a $4\times 4$ grid of unit squares.

We choose any $2$ of these $16$ squares.

Total number of ways to choose 2 squares

$\binom{16}{2} = \frac{16\cdot 15}{2} = 120$

Count pairs having a side in common

Two squares have a side in common if they are adjacent horizontally or vertically.

(i) Horizontal adjacent pairs

In each row of $4$ squares, the number of horizontal adjacent pairs is $3$. Since there are $4$ rows, $4\times 3 = 12$

(ii) Vertical adjacent pairs

In each column of $4$ squares, the number of vertical adjacent pairs is $3$. Since there are $4$ columns, $4\times 3 = 12$

Hence total pairs with a common side: $12+12=24$

Count pairs with no side in common

$120-24=96$

Required probability

$P(\text{no side in common})=\frac{96}{120}=\frac{4}{5}$

Compare with options

$\frac{4}{5}$ matches Option B.

Comparison with stored correct answer

Stored correct answer is B, which agrees with the derived result.