Consider a grasshopper located at stone wants to go to stone 9. The grasshopper can jump either one or two stones at a time, and it does not take any steps back. This means that it can go to 9 following the path 0-1-3-5-6-8-9, or 0-2-3-5-6-7-8-9, or 0-1-2-3-4-5-6-7-9 etc.

How many distinct paths can the grasshopper take to stone 9?

 

Consider a grasshopper located at stone wants to go to stone 9. The grasshopper can jump either one or two stones at a time, and it does not take any steps back. This means that it can go to 9 following the path 0-1-3-5-6-8-9, or 0-2-3-5-6-7-8-9, or 0-1-2-3-4-5-6-7-9 etc.

Assuming that jumping one or two stones are equiprobable, what is the probability that the grasshopper visits stone 6?