14. Toss a coin, each time it lands on heads you get 1 point, and on tails you get 2 points. Repeatedly toss this coin, then the probability of getting exactly $n$ points is $\qquad$
Let the probability corresponding to the event of "scoring exactly $n$ points" be $p_{n}$, then $p_{1}=\frac{1}{2}, p_{2}=\frac{1}{2}+\frac{1}{2} \cdot \frac{1}{2}=\frac{3}{4}$, $p_{n}=\frac{1}{2} p_{n-1}+\frac{1}{2} p_{n-2} \Rightarrow p_{n}+\frac{1}{2} p_{n-1}=p_{n-1}+\frac{1}{2} p_{n-2}=\cdots=\frac{3}{4}+\frac{1}{4}=1$, thus $p_{n}=-\frac{1}{2} p_{n-1}+1 \Rightarrow p_{n}-\frac{2}{3}=-\frac{1}{2}\left(p_{n-1}-\frac{2}{3}\right) \Rightarrow p_{n}-\frac{2}{3}=-\frac{1}{6}\left(-\frac{1}{2}\right)^{n-1}$ $\Rightarrow p_{n}=\frac{2}{3}+\frac{1}{3}\left(-\frac{1}{2}\right)^{n}\left(n \in \mathbf{N}_{+}\right)$.