7. In a $100 \times 100$ square grid, any rectangle parallel to the grid sides is chosen. The probability that this rectangle is a square is
7. $\frac{67}{5050}$.

In an $n \times n$ square grid, the number of squares with side length $k$ is $(n+1-k)^{2}$, so there are
$$
\sum_{k=1}^{n}(n+1-k)^{2}=\frac{n(n+1)(2 n+1)}{6}
$$

squares in total.
Therefore, the required probability is
$$
\begin{array}{r}
P=\frac{\frac{n(n+1)(2 n+1)}{6}}{\left(\mathrm{C}_{n+1}^{2}\right)^{2}} \\
=\frac{2(2 n+1)}{3 n(n+1)}=\frac{67}{5050} .
\end{array}
$$