Consider the $$6 \times 6$$ square in the figure. Let $$A_1, A_2, \ldots, A_{49}$$ be the points of intersections (dots in the picture) in some order. We say that $$A_i$$ and $$A_j$$ are friends if they are adjacent along a row or along a column. Assume that each point $$A_i$$ has an equal chance of being chosen.