2. Choose any three vertices from a regular nonagon to form a triangle, then the probability that the center of the nonagon is inside the triangle is
Solve $\frac{5}{14}$.
Analysis As shown in the figure, the triangles containing the center in a regular nonagon have the following three shapes:
For (1), there are 3 cases; for (2), there are 9 cases; for (3), there are 18 cases; hence the required probability is
$$
P=\frac{3+9+18}{C_{9}^{3}}=\frac{5}{14}
$$