Please answer the question in full, provide any equations or diagrams used to come to your final answer.
In the board game Settlers of Catan, you use a pair of standard 6 sided dice. On each turn the player starts by rolling the dice. If the roll is a 7, the robber moves.
- What is the probability that the robber does not move after 6 turns?
- What is the probability that the robber has moved at least 3 times after 9 turns?
What is the probability that the robber moves for the third time on the ninth turn?