The figure shows a square divided by 6 equally-spaced horizontal and 6 equally-spaced vertical lines.
Hence each side has 7 grid points, giving an overall lattice of $$7 \times 7$$ points.

Total number of intersection points
$$= 7 \times 7 = 49.$$
Label these points $$A_1, A_2, \ldots, A_{49}$$.

A pair of points is called “friends” if the two points are directly adjacent either in the same row or in the same column (vertical or horizontal neighbours only).

Step 1 - Count all possible pairs of points
For 49 distinct points, the total number of unordered pairs is
$$\binom{49}{2} \;=\; \frac{49 \times 48}{2} = 1176.$$

Step 2 - Count horizontal friend pairs
• Each row contains 7 points.
• Adjacent pairs within one row: $$7-1 = 6$$ pairs.
• There are 7 such rows.
So the number of horizontal friend pairs is
$$7 \times 6 = 42.$$

Step 3 - Count vertical friend pairs
By symmetry, each of the 7 columns also has 7 points and therefore 6 adjacent vertical pairs. Thus
$$7 \times 6 = 42$$ vertical friend pairs.

Step 4 - Total friend pairs
$$42 + 42 = 84.$$

Step 5 - Probability that a randomly selected pair is a friend pair
$$p = \frac{\text{number of friend pairs}}{\text{total pairs}} = \frac{84}{1176} = \frac{1}{14}.$$

Step 6 - Compute $$7p$$
$$7p = 7 \times \frac{1}{14} = \frac{1}{2} = 0.50.$$

Therefore, the required value of $$7p$$ is 0.50.