Possible Duplicate:
A probability question
Needing a little help with the following problem,
A player tosses a fair coin and is to score one point for every head turned up and two points for every tail. He is to play until his score reaches or passes $n$. Find the probability that his score is exactly $n$.
Here's how I would approach the problem.
Let $X$ be the number of points scored in the coin toss. Then $X = X_{1} + \cdots + X_{i}$.
$ X_{j} = \begin{cases} 1, & \text{if the } i^{\rm th} \text{ trial is a success}, \\ 2, & \text{otherwise}. \end{cases} $
So $E[X] = i \cdot E[X_{1}] = ??$
Here is where I got stuck...
Anybody got any idea on how to proceed?