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 $A_{8}$.
Answer: $\quad P(A)=\frac{1}{7} \cdot\left(\frac{5}{6^{2}}+\frac{21}{6^{3}}+\frac{35}{6^{4}}+\frac{35}{6^{5}}+\frac{21}{6^{6}}+\frac{7}{6^{7}}+\frac{1}{6^{8}}\right)$