4. Flea Kuzya can make jumps from each vertex of a regular tetrahedron $A B C D$ to the three adjacent vertices, and the choice of these vertices is random and equally probable. Kuzya started jumping from vertex $A$ and, after 2024 jumps, ended up not in vertex $A$. What is the probability that this could happen?
Answer: $\quad P(A)=\frac{3^{2024}-1}{4 \cdot 3^{2023}}$.