4. Pete throws a die several times onto the table and counts the sum of the points that come up. For any natural number $n$, the event $A_{n}$ occurs if this sum equals $n$. Find the probability of the event $A_{9}$.
Answer: $\quad P(A)=\frac{1}{8} \cdot\left(\frac{4}{6^{2}}+\frac{25}{6^{3}}+\frac{56}{6^{4}}+\frac{70}{6^{5}}+\frac{56}{6^{6}}+\frac{28}{6^{7}}+\frac{8}{6^{8}}+\frac{1}{6^{9}}\right)$