2014 UNCO Math Contest II Problems/Problem 9


In the Queen’s croquet, as described in Problem $8$, what is the probability that the ball hits the goal post the $n$th time the ball is hit?


Zero probability for $n=1$ and $\frac{F_{n-1}}{2^{2n}}$ for $n\ge 2$, where $F_{n-1}$ is the $(n-1)^{st}$ Fibonacci number.

See also

2014 UNCO Math Contest II (ProblemsAnswer KeyResources)
Preceded by
Problem 8
Followed by
Problem 10
1 2 3 4 5 6 7 8 9 10
All UNCO Math Contest Problems and Solutions