2. Let the edge length of the regular tetrahedron $ABCD$ be 1 meter. A small insect starts from point $A$ and moves according to the following rule: at each vertex, it randomly chooses one of the three edges connected to this vertex and crawls along this edge to another vertex. What is the probability that it returns to vertex $A$ after crawling 4 meters? $\qquad$
2. $\frac{7}{27}$ Detailed Explanation: After crawling 4 meters, the total number of paths is $3^{4}=81$. For the paths that return to vertex $A$, if the vertex reached after crawling 3 meters is $A$, there are $3 \cdot 3=9$ such paths. If the vertex reached after crawling 3 meters is not $A$, there are $3 \cdot 2 \cdot 2=12$ such paths. In total, there are 9 $+12=21$ paths, thus the required probability is $\frac{21}{81}=\frac{7}{27}$.